Rebel Labour MPs vowed to continue their fight against the higher education bill in the next stage as the rush to get on to the committee began.
Ian Gibson, a key rebel leader, said: "We will be pushing for the removal of variable fees at committee stage. We also want the repayment level raised from £15,000 to £20,000."
He said that if the bill did not meet rebel demands it could face defeat at the third reading.
Graham Allen, who had originally opposed variable fees but switched to backing them before Christmas, said: "I have put my name forward to go on the committee. We now need to have a really open process to debate and improve this bill."
He said that the involvement of the Parliamentary Labour Party had considerably improved the original white paper proposals.
In a direct challenge to those who continued to oppose the bill outright, he released statistics showing how many students would now be eligible for the full £2,700 grant in rebel MPs' constituencies. For George Mudie's Leeds East constituency it is 55.67 per cent, for Ian Gibson's Norwich North 51.28 per cent and for Paul Farrelly's Newcastle-under-Lyme 47.9 per cent.
Whips from all parties are expected to decide in the next few days who to put on the committee, which it is anticipated may comprise about 18 MPs.
Alan Whitehead, whose paper with Peter Bradley brought about significant government concessions, said: "In principle I would like to be on the committee but as I am already on one I am having to look at the possibility of a transfer."
He said that it was crucial to get government concessions written on to the face of the bill. "Many of the MPs who abstained did so because I believe they thought that without their concessions the bill would come back at report stage. To get this past third reading we have to make sure that does not happen," he said.
Mr Whitehead was originally opposed to top-up fees but now believes that they have been reduced to a standard fee with discounts and that it is crucial to get the upfront grants and postgraduate repayments through Parliament.
In all, 72 Labour MPs voted against the bill, making it the largest rebellion on domestic legislation since 1997 and the joint-largest revolt by government MPs on a second reading of a bill since 1945.
Eighteen Labour MPs abstained from the vote, including Robin Cook and Cambridge MP Anne Campbell. One Conservative MP, Robert Jackson, voted with the government.
The crucial switch by rebel Nick Brown at the last minute is believed to have persuaded a handful of Gordon Brown supporters - Barbara Roche, Bob Blizzard, Angela Eagle and Clive Betts - to swap sides, just saving the bill.