Cook - who endured a rough time in Australia and New Zealand, with one massive score of 244 not out at Melbourne but just 155 runs in his other 12 innings combined - said that England's suspicions had been especially aroused on the final day of the third Test at Perth, when Australia overcame a three-hour rain delay to pick off England's remaining six wickets for an Ashes-sealing victory.

The day had begun with England once again up against it on 132 for 4 - needing a further 128 to make Australia bat again - but with their two first-innings centurions, Dawid Malan and Jonny Bairstow standing firm for the fifth wicket. And, when the start of play was delayed after water seeped through the covers onto the wicket, the prospect of an unlikely escape presented itself.

In the end, Australia rattled through England's lower order within a further 33 overs, Hazlewood claiming 5 for 48, but Cook admitted that there had been one or two doubts in the England dressing-room as to the methods that their opponents had been using.

"Yeah, a little bit," Cook said, when asked if England had been suspicious. "We did think in Perth, when the outfield was wet after the rain, how had they managed to get the ball reversing? I didn't see anything, [but] we've been pretty good on the ball, managing the ball so that it can reverse swing at certain times. Jimmy [Anderson] is obviously very good at reverse swinging, we got it going a touch at Melbourne either way, but with those drop-in pitches we didn't get it going massively."

However, Cook also admitted that "no one really understands" the mechanics of reverse swing, and conceded that a simpler answer might be that they had been out-performed by better, and faster, bowlers - just as Australia themselves had been in the great Ashes contest of 2005.

"We were curious in that series at certain moments but we couldn't get the ball up to 90mph and they consistently could," he said. "That was the thing back in 2005. Obviously in England we had Simon Jones and Freddie [Flintoff] who were quicker than the Aussies, and they managed to get the reverse swing and the Aussies didn't, so we have to be very careful there."

Cook, who was speaking at an event to celebrate the return of Yorkshire Tea National Cricket Week with cricket charity, Chance to Shine, was put on the spot during an assembly with local primary-school children when one of them asked him his opinion of "Australia's cheating" during the recent Cape Town Test. In an improvised response, he likened the act to diving in football, in that there are rules in place, but players will still push the boundaries of what is acceptable.

"It's not for me to comment on the punishments," he told the media afterwards. "I just think it was a real reminder, watching the whole thing, of what people want to watch in sport. It was the same as cycling, and the match-fixing in one sense, when people buy tickets to watch sport, they want to see, no matter who is playing, it's done in a fair way.

"It was an amazing public outcry, and sometimes under the pressure of playing, when it feels so important to you because it's your profession, your livelihood, sometimes winning or losing can take over. Win lose or draw, if you try your hardest with no external things, you win or lose that way. But it's wrong for anyone here in the cold light of day to criticise, because people do make mistakes."

Cook's own mistakes were ones of the technical variety, as he looked back with regret on a winter of underachievement, which culminated in scores of 5, 2, 2 and 14 on the New Zealand leg of the winter - for an overall series average of 5.75, the lowest by a distance of his 154-Test career.

"In New Zealand I just never got going," he said. "That tour kind of passed me by before I even got past the fifth over, which is frustrating in every form of life, when you go all that way, you train, and you just don't turn up.

"It does happen. If you play 100-odd Test matches, there's going to be little periods when you don't score the runs. I've always managed to turn it around. The last six months, I've never been quite so inconsistent. I still averaged 47 last year. I could still average 47 this year. Go back to India 2011, I was averaging 5 in the first two Test matches, ended up with 290 at Edgbaston, and the whole series changed.

"But since I've come home I've started to look at my preparation. Have I got my preparation right? Do I need to change things? Because that's the right way to do it. I will never sit here and say I've cracked the game or will ever be perfect."

Alastair Cook plays cricket with schoolkids during a Chance to Shine / Yorkshire Tea event Getty Images

Cook insisted, however, that his hunger to "go back to the well" was undiminished, even after 12 years of Test cricket including a remarkable 152 consecutive Test appearances.

"What is the well?" he said. "Why, just because you've played 150 games, do you have to talk about a well? One thing I do know is that it doesn't get any easier. I remember talking to a psychologist, watching Jacques Kallis, and he'd just scored his 12,000 runs, and thinking: 'he's all right, he's cracked the game, it doesn't matter what he does, he can just turn up and bat'.

"And the bloke said to me: 'mate, you're wrong. If you ever get there, it'll be just as hard as when you started'. But while I still want to get out and bat and put myself under pressure and sit in the changing room, I've got to do it."

That challenge, he said, would be no different even with a new National Selector in Ed Smith to impress.

"My job never changes," he said. "It's to score runs at the top of the order and, if you don't score runs, there's been times throughout my career where people have questioned my place like they are questioning it now - that hasn't changed.

"If someone taps me on the shoulder and tells me they don't want me to open the batting for England, it is going to hurt at this precise moment of time because I want to carry on. But it's his job, and I very much understand. I am sure he will have some different ideas so we will wait and see."

Yorkshire Tea National Cricket Week will take place 18th - 22nd June, giving thousands of children across the country the opportunity to play and learn through cricket.