Harry Brook hopes he has given England's selectors a headache with his performances in Pakistan, but believes Jonny Bairstow should return to the team when he recovers from injury.

Brook scored 111 as England posted a first innings total of 354 on day two of the third Test in Karachi, taking a first innings lead of 50, though the hosts cut that to 29 after finishing the day on 21 without loss.

The 23-year-old has made three centuries in three Tests during the tour of Pakistan, vindicating captain Ben Stokes' decision to pick him as a replacement for Bairstow, who enjoyed a free-scoring 2022 before a freak leg injury ruled him out for several months.

Bairstow will be eyeing a return ahead of next year's Ashes series, and Brook says he would back him for an immediate recall, though hopes his own scintillating form has thrown a wrench into the plans of England's selectors.

Brook also broke Alastair Cook's record of 450 runs from 2015-16 to score the most runs by an English men's cricketer in an overseas Test series against Pakistan.

"Most selectors say they like headaches, so hopefully I've caused a very big migraine," he said after the close of play on Sunday. "It's too hard to say at the moment.

"I think Jonny is one of the best players, if not the best player, in the world. He was this summer anyway. For me, he comes straight back into the side.

"Obviously, I'm not selecting the team, but he's such a big player for the side, and he has been for so many years."

Brook acknowledged he had exceeded his own expectations with his form in Pakistan, after his latest century steered England ahead in the third and final Test of a series they have already won.

Having also helped England to the T20 World Cup in Australia, Brook said he is enjoying his achievements on tour.

"I actually said to one of my mates before I came out here that I would love to get two hundreds out here," he added. "So obviously to go one better is a very nice feeling."