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The latest person to add his voice to the calls for Cook to stand down was Kevin Pietersen, who suggested in a column for The Daily Telegraph that Cook needs to resign the captaincy and take time out from playing for England to regain his form.
Cook, however, is having none of it.
"I keep saying as I keep saying it seems in every press conference at the moment - I'm desperate to carry on because I love being England captain.
"It's a huge honour and as I said when first took over, I just want to throw everything into it.
"And, until that time where I don't feel I can carry on doing it or when someone taps me on the shoulder, then that's what I'm going to do."
Responding to a question about whether he is aware of the criticism levelled at him and whether he is affected by it, he remained defiant.
"Does it affect me? I'd rather not say it.
"But again I'm quite a strong-willed guy who doesn't take too much notice really, of the media.
"Because we understand it and I have to concentrate on myself these five days and not what people say in the commentary box."
Reflecting on the summer so far, which has seen England fail to win either of the four Tests they have played, Cook admitted it had been frustrating.
"It has been a really tough summer because we haven't won as many games of cricket, the frustrating thing is we have been getting ourselves in situations - in four Test matches where we're ahead of the game by quite along way but we haven't been able to force the result," he said.
"So we must be doing a lot of things very well but at the moment, the crucial sessions where we've need to stamp our authority, to get that win we haven't managed to take.
"It's bubbling under - the longer it goes without a win, it becomes harder and harder."
And with England 1-0 down to India going into the third Test after a 95-run defeat at Lord's, Cook is keen to remind everybody that last year they bounced back from such a margin to win the series.
"Without doubt it gives you confidence, I remember going into a press conference in Mumbai looking after looking at that wicket, a few ex-players were saying, 'We can't play spin' and 'We're going to lose four-nil' so to turn it round, everyone says that's one of my greatest achievements as a player - to be part of that series and no one remembers that we got hammered in the first game.
"Everyone remembers that we won the series. So, we're one-nil down, and if we win the series, at the end of the series it will be a great thing."
Videos courtesy of SNTV.
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