Alastair Cook suffered another double whammy in his deepening England captaincy nightmare as a record-breaking last-wicket partnership by India was followed by yet another failure with the bat.

Cook spent almost three hours in an increasingly desperate quest to dismiss either of the India tailenders Bhuvneshwar Kumar and Mohammed Shami – who came into the match with a Test batting average of 3.33 – as a sun-baked Trent Bridge crowd grew increasingly frustrated.

After India were finally all out for 457, there was a grim inevitability about what followed when Cook launched England’s reply late in the day, even though no one would have predicted the manner of his latest demise – bowled behind his legs for five by Shami after the ball had deflected off his thigh pad, leaving the rookie pair of Sam Robson and Gary Ballance to begin repairing the damage by reaching 43 for one at the close.

That extends Cook’s run of innings since his last Test century, against New Zealand at Headingley last May, to 25, and he has averaged only 24 in that period. Recent statistics are even more worrying, as he has now scored 97 runs in his last seven Test innings, and 83 in five this summer.

Cook has been emphatic in ruling out the possibility of resignation at increasingly regular intervals, but has admitted himself that he needs runs quickly to justify his continued selection. His future as captain is undeniably a live issue, even if his captaincy in this match has earned more praise than criticism, in contrast to the second Test defeat by Sri Lanka last month.

“He’s just in one of those places at the moment,” said Stuart Broad, who has been forced to speak in defence of his captain more often than Cook himself in recent days – and was “asleep in the bath” when Cook was dismissed, having earned the admirable figures of 33-13-53-2. “When you’re in a bit of a rut things go against you. I can count on one hand the number of times I’ve seen a batsman bowled off the thigh pad. They generally go to fine leg for one.

“When you get out like that there’s not a lot you can do. He was chatting away, he was chirpy. Obviously disappointed not to have made a big contribution, but he’d be more disappointed if he’d have nicked off from fifth stump.”

Broad was scathing in his criticism of the pitch, even at his home county ground, arguing that restricting India to 457 was a reasonable effort despite the partnership of 111 between Kumar and Shami, which was their new record for the 10th wicket against England.

“Indian wickets are faster than that,” he said when it was suggested that the conditions might have been prepared to suit the visitors. Once that ball is 50 overs old it’s not doing a lot out there. We tried everything – a few bouncers, go full at the stumps. But if you can’t bowl a bouncer it takes off a lot of the threat.

“I thought we all stuck at it brilliantly, there was no moping or swearing, and 450 is a decent score but not 600 which could easily have happened on that wicket. There was only one moment that got me, when I was bowling my 30th over and a bloke on his fifth pint shouted ‘bend your back Broad’.

“The best thing that’s happened is that Trent Bridge have come out and said look, it’s our mistake, and apologised for the pitch. There’s not much more can be said about it. Trent Bridge is renowned for exciting cricket, but we’ve not seen a lot of that. Let’s just hope that other grounds don’t follow suit.”