Virat Kohli's century helped all but clinch the third Test for India on day three as England were set the task of a record-high chase at Trent Bridge.

The India captain began the day at the crease and contributed to a 113-run, 289-ball stand for the third wicket with Cheteshwar Pujara (72) en route to a knock of 103 and a 521-run lead after a declaration.

With nine overs and two days remaining, England required a fourth-innings total far beyond the West Indies' record successful chase of 418 in a 2003 Test against Australia.

And India's grasp on the third match - a belated foothold in a series they trail 2-0 - was scarcely loosened by the embattled hosts' feat of reaching the close on 23 without loss, still 498 runs short of victory.

Another miserable day beckoned for England when Pujara was dropped on 40 by Jos Buttler at slip, failing in a one-handed catch low to his left.

Pujara and Kohli kicked on, while the hosts lost wicketkeeper Jonny Bairstow to injury as he took a blow to his left hand after misjudging a James Anderson delivery. Buttler took the gloves and scans confirmed a small fracture to Bairstow's middle finger.

The two India batsmen reached their respective half-centuries with singles in successive overs and continued beyond lunch, before the partnership was finally ended as Pujara was caught by Alastair Cook off Ben Stokes.

However, vice-captain Ajinkya Rahane, who partnered Kohli for 159 - India's highest stand of the series - in the first innings, arrived in the middle and England made no further progress before tea as the lead stretched beyond 400.

And Kohli's second hundred of the tour arrived with a four shortly after a thick edge flew through Keaton Jennings' hands at gully.

The skipper did not last much longer as he was trapped lbw by Chris Woakes, with Rishabh Pant (1), the next man in, quickly following as Cook caught him off the bowling of Anderson. 

That slight wobble did little to slow India down and only after Adil Rashid (3-101) had removed both Rahane (29) and Mohammed Shami (3), with Hardik Pandya unbeaten on 52, did Kohli call the innings to an end at 352-7.

Cook (9 not out) and Jennings (13 no) at least ensured England made it to day four without further damage, but a daunting challenge awaits in Nottingham.