Kate Hoey on the the leave campaign trail with then Ukip leader Nigel Farage in June. Photograph: Ben Stansall/AFP/Getty

The contest to chair a powerful committee of MPs which will scrutinise the government’s Brexit deal will be a two-horse race between Labour’s former shadow foreign minister Hilary Benn, who is pro-remain, and the prominent leave campaigner Kate Hoey.

Benn, who campaigned vigorously for remaining in the EU, was backed to chair the Exiting the European Union select committee by the former Labour leader Ed Miliband and other senior colleagues, including Angela Eagle, Dan Jarvis and Andy Burnham.

Benn also has support from the pro-EU Tories Anna Soubry and Andrew Mitchell, as well as Sarah Wollaston, who changed her mind to back remain in the late stages of the referendum campaign.

Hoey, a long-time vocal advocate for leaving the EU, joined Ukip leader Nigel Farage’s Leave.EU group to make the “left-wing case” for exiting. The MP for Vauxhall, south London, counts both leave and remain-backing MPs among her supporters, including Labour Brexiters John Mann, Frank Field and Gisela Stuart, the Tory leave supporter Theresa Villiers, and the pro-remain former SNP leader Alex Salmond.

Benn said he believed that the referendum decision had to be implemented and said he would seek to scrutinise and offer advice to the government. “Our aim should be to minimise the risks and uncertainty for business, protect the things that the British people value and make the most of the opportunities,” he said.

Hoey said: “I campaigned passionately for a leave vote, and agree that those of us who did so have a particular responsibility to make a success of it. I am putting myself forward as chair of this new committee because I want to be a constructive part of making this work.”

Only Labour MPs were eligible to stand for the committee chairmanship, which scrutinises David Davis’s department. A separate international trade select committee to examine Liam Fox’s department has been assigned an SNP chair, with Angus MacNeil standing unopposed.

MPs will vote for their preferred candidate on Wednesday morning, with results announced that afternoon.

Other key committee positions are also being elected, with four Labour MPs competing to replace Keith Vaz as chair of the home affairs select committee. All four are former members of the shadow cabinet: Yvette Cooper, Chuka Umunna and Caroline Flint under Ed Miliband, and Paul Flynn under Jeremy Corbyn.

Cooper, who is backed by MPs including Harriet Harman and Dominic Grieve, said there were key Brexit issues for the committee to scrutinise, including security co-operation, cross-border policing and immigration.

Umunna, already a member of the committee and backed by committee colleague Naz Shah, as well as the former Lib Dem leader Nick Clegg, also said Brexit would be a focus, and said he had spent time visiting Boston in Lincolnshire, talking to people in the area which recorded the highest leave vote, as well as in his own constituency of Lambeth which notched up the highest remain vote.

Flint, who was a home office minister in the Labour government, has been nominated by a number of former shadow ministers including Angela Eagle, Mary Creagh and Liz Kendall. In a statement, Flint said she wanted to take a rigorous look at immigration policy as chair. “Good policy must reflect the variety of experiences from Cornwall to Caithness or Conwy, not simply the loudest voices or most powerful interests,” she said.

Of the four, only Flynn has served under the current Labour leader, Jeremy Corbyn. The MP said he had “an apprenticeship of 29 years serving on select committees” and boasts support from the left of his party, including chief whip Nick Smith, shadow justice secretary Richard Burgon and shadow business secretary Clive Lewis.

Five Tory MPs are competing to chair the science and technology committee: Victoria Borwick, Stephen Metcalfe, Dan Poulter, Derek Thomas and Matt Warman.