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Protesters have said they were "lucky" to get visas for Ukrainian family members after negotiating the "confusing" UK application process.
People gathered in Bath at the weekend to raise funds for charities supporting those caught up in the war in Ukraine.
Some said they were fearful people were dying while waiting to get visas enabling them to seek refuge in the UK.
The Home Office said it was "doing everything possible" to ensure a rapid service.
Zhenya Shkil, who lives near Bath, said getting a visa for her 12-year-old cousin was "complex".
"I have family in East Ukraine in quite a dangerous location near the power station," she said.
"Luckily, thankfully, we got visas for Olesksandr to come and stay with us here.
"The application form is really complex and confusing," she added.
"There is a mixture of questions about sponsors and applicants and everyone makes mistakes. There's no way you can deal with it.
"It takes about an hour to fill in one form with me on the phone with someone talking me through."
Jura Everauskite, who also attended the demonstration on Saturday, said she did not "want the public to forget that war is happening".
"The visas scheme in the UK is just unacceptable. People have to wait weeks for their visas while people are dying," she said.
"We want to protest that. It doesn't make sense.
"We are getting a lot of support and there are a lot of people who want to host refugees in Bath."
