Prime Minister Boris Johnson has vowed to leave the EU "come what may" by the 31 October - the date the UK must depart if no deal has been reached.
How could you be affected if the UK does leave the EU without an agreement?
What you find on the supermarket shelves could well be where you see the first effects.
Almost 30% of our food currently comes from the EU, and it is likely that some foods, such as fresh vegetables and fruit, will become more scarce and more expensive in the event of no deal.
Increased import taxes and transport delays could all mean a rise in prices. And if a no-deal Brexit was followed by a fall in the value of the pound, that would also have the same effect.
Supermarkets themselves have warned that there could be empty shelves and higher prices.
And Bank of England governor Mark Carney has said that, in a worst-case scenario, our shopping bills could increase by 10%.
The government has said that while a no-deal Brexit alone won't lead to food shortages, consumer behaviour could. Panic buying could mean food retailers run short of some products.
In preparation, supermarkets say, they have been stockpiling some foods - but they are unable to do that for some fresh fruit and veg.
Sainsbury's has also said October would be one of the worst times for the UK to exit the EU without a deal because warehouse capacity is already strained by the seasonal stock build-up ahead of Black Friday and Christmas, limiting supermarkets' ability to store goods ahead of Brexit.
Shoppers planning to buy from companies based in the EU, Norway, Liechtenstein and Iceland after a no-deal Brexit have also been warned credit and debit card charges may be higher and payments may take longer.
Millions of people from the UK travel abroad each year - the vast majority of journeys made to Europe.
If you are planning to make a journey to an EU member state after Brexit, the government is advising you to check you have the right paperwork.
Travel to Ireland will not change, even if there's no deal. You'll continue to be able to travel and work there in the same way as before.
Passports
The government is advising you to make sure your passport is valid for at least six months if you are travelling to most countries in Europe - the full list is here.
Until recently, UK citizens who renewed their passport before it expired could have up to nine months of the remaining validity added to their new travel document.
But the government has now warned that this time carried over may not count towards the six-month requirement after a no-deal Brexit. You can check if your passport has enough time left with this government tool.
You'll need to renew your passport before travelling if you do not have enough validity left. It usually takes three weeks.
Visas
You won't need a visa for stays of up to 90 days out of any 180-day period in the EU or Iceland, Liechtenstein, Norway and Switzerland (the European Economic Area). However, you may need a visa or permit to stay for longer, or to work or study.
When new rules are confirmed, information about visa requirements will be on each country's travel advice page.
Border control
The government has also advised that at EU borders you may need to:
European health cover
In addition, if there is no deal, then in theory the cover provided by your European Health Insurance Card (EHIC) would cease to exist.
The government is advising travellers "whether there's a deal or not" to "get appropriate travel insurance with healthcare cover".
Travel
However you intend to travel, in the event of no-deal Brexit, the government says, you should check before you leave for any delays or disruption.
If you intend to drive in the EU, you'll need some extra documents:
The government says flights, ferries and cruises, the Eurostar and Eurotunnel and bus and coach services between the UK and the EU will continue to run as normal.
An earlier government assessment had warned of long queues at London's St Pancras International, the main Eurostar terminal in the UK, but Eurostar bosses have said they are working to ensure their services run as smoothly as possible.
However, the government does warn some bus and coach services to non-EU countries, such as Switzerland or Andorra, may not be able to run.
Bank cards
If you have a UK bank account and intend to use your bank card to pay for goods and services while you are in the EU as well as Iceland, Liechtenstein and Norway, the government has warned that it may become more expensive.
Ministers and NHS leaders say every effort is being made to ensure there will be enough medicines and clinical equipment available in the event of delays to imports from the EU.
However, the Royal Pharmaceutical Society warned in January that pharmacists were struggling to obtain common medicines - including painkillers and anti-depressants.
While there are regular fluctuations in medicine supplies, there are concerns a no-deal Brexit could make shortages worse.
About three-quarters of the medicines and most of the clinical products we use come from or via the EU.
The government says the main risk to supply is reduced traffic flow between the ports of Calais and Dover or Folkestone.
Cabinet Office Minister David Lidington has said there are renewed no-deal preparations under way, including attempts to secure "extra warehouse space" for medicines.
Other measures taken by the government include:
About 1.3 million UK-born people live in the other 27 EU countries.
The UK government has requested that EU countries reciprocate its promise to uphold the rights of EU citizens in the UK, meaning UK citizens living in the EU would be able to continue their lives broadly as now.
In event of no deal, this would ensure they would have continued access to employment, healthcare, education, benefits and other services.
The government advises UK citizens living in the EU to subscribe to updates from the relevant country advice pages.
Health
UK nationals living in, working in, or visiting the EU may find their access to healthcare in EU member states will change after the UK leaves the EU with no deal. This will depend on decisions made by each country.
However, the UK government says it is seeking bilateral agreements to maintain healthcare rights, as a top priority.
Information on how to access healthcare abroad can be found on the NHS website.
Pensions
The UK government will continue to pay state pension, child benefits, and disability benefits to eligible UK nationals in the EU.
Tax
The UK's exit from the EU will not change existing double taxation arrangements, which apply to EU countries.
These ensure everyone - not just British citizens - living in a country that has a treaty with the UK will not pay tax in two countries on the same income or gain - and determine which country has primary taxing rights.
The UK government has reached an agreement with the EU, as well as Norway, Iceland, Liechtenstein, and Switzerland, that will protect the rights of EU citizens and their family members living in the UK.
There are about 3.7 million EU citizens living in the UK.
Importing goods from the EU is likely to get more expensive when free movement of goods ends with the UK's departure.
As a member of the EU, UK firms don't have to pay extra duties, taxes or have customs checks on goods travelling to or from the EU.
But after a no-deal Brexit, new rules will apply. UK businesses will need to apply the same processes to EU trade that apply when trading with the rest of the world.
In March, the government published a 1,477-page document outlining their plan for tariffs in the event of a no-deal Brexit.
A tariff is a tax applied to goods that are traded on international markets. Mostly, they are applied to imported goods by the country importing them. But there can also be tariffs on exported goods.
Under the temporary scheme, 87% of imports by value would be eligible for zero-tariff access. At the moment, 80% of imports are tariff free.
Tariffs would be maintained to protect some industries, including agriculture. Beef, lamb, poultry and some dairy products would receive protection.
Most commentators and industry experts agree uncertainty created by the Brexit process is causing buyers and sellers to sit tight, causing a slowdown in the housing market.
Annual house price growth has been below 1% for the six months in a row to May, according to data compiled by Nationwide.
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said that Brexit uncertainty was likely to have "instilled some caution in buyers".
The Bank of England says the impact of the UK leaving the EU on the housing market could be significant.
It has said house prices could fall by up to 30% from pre-Brexit levels if there was no deal, or a "disorderly Brexit".
Property agents Savills suggest buyer confidence will have a bigger role to play than affordability in house price movements this year.
Using your mobile in the EU may be more expensive in the event of a no-deal Brexit, the government has warned.
The amounts EU mobile operators would be able to charge UK operators for providing roaming services would no longer be regulated after Brexit.
However, some mobile operators (3, EE, O2 and Vodafone) have said that they have no current plans to change their approach to mobile roaming after the UK leaves the EU.
If your mobile operator is proposing to reintroduce surcharges for roaming, or change the terms on which it offers roaming, the government advises you to understand how to turn off data roaming on your mobile phone.
Transport Secretary Chris Grayling has said there could be freight traffic disruption in Kent in the event of a no deal, if additional customs checks are introduced in Calais, Coquelles and Dunkirk - where freight services disembark.
At the moment, freight vehicles going through Dover are subject to passport and security checks.
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But under a no-deal scenario, EU-bound lorries will also need to complete customs declarations, and certain goods may also require physical checks, and this could lead to bottlenecks.
In this scenario, a traffic management system known as Operation Brock would come into force on a section of the M20. Traffic would be allowed to flow in both directions on the same carriageway, while lorries would be left queuing on the other side.
If that proved to be insufficient, a disused airfield near Ramsgate would be used as a lorry park, and if further capacity was still required, the M26 could also be used.
Kent County Council says it has employed extra staff and stockpiled supplies in preparation for six months of disruption in the event of no deal.
More than 16,000 British students studied on placements organised by the Erasmus study abroad scheme - in place since the 1980s - in 2016-17.
UK universities say they would expect a similar number to be planning to do the same this coming academic year.
The government is committed to funding everything already agreed, so people who have already started Erasmus trips will be able to continue them.
But if the UK leaves the EU without a deal before the exchanges for the next academic year have been finalised, then the government would need European agreement to keep taking part. It has issued a technical note explaining this.
That is true for both UK students planning to go to EU countries, and EU nationals hoping to come to the UK.
Meanwhile, Universities UK has launched a campaign supporting opportunities for studying abroad.