Senior Conservatives have backed a plan to force a vote in the Commons aimed at pushing Theresa May into negotiating for Britain to stay in a customs union with the EU after Brexit.

Ex-cabinet ministers Nicky Morgan and Dominic Grieve teamed up with other senior MPs, including Labour’s Yvette Cooper and Rachel Reeves, to force the vote next week.

Less than 24 hours ago the government was defeated in the House of Lords on a motion also aimed at keeping the UK in a customs union.

While the Commons vote due on Thursday will not be binding on Ms May, if it is passed it will stand as a show of strength from soft-Brexit backing MPs ahead of other binding votes on the customs union in the weeks ahead.

Thursday’s motion demands the government “include as an objective in negotiations on the future relationship between the United Kingdom and the European Union the establishment of an effective customs union between the two territories”.

It has been backed by the chairs of major Commons committees, Ms Cooper, who heads the Home Affairs Committee and, Ms Morgan, from the Treasury Committee.

They said in a joint statement: “With just six months to go before the Brexit deal needs to be concluded, we are running out of time for parliament to help to shape the negotiations.

Boris Johnson: Northern Irish border being used to try and keep the UK in the customs union

“Yet many of our backbench committees have forensically gathered evidence on different Brexit options and the practical implications.”

They added: “If parliament stays silent until after the deal is done, that is just a recipe for conflict and regret later on. Far better for us to debate this properly now and let parliamentarians express their view before it is too late.”

The motion is also supported by Tory MP Sarah Wollaston, who chairs the Health and Social Care Committee, and Bob Neill, of the Justice Committee, Labour’s Hilary Benn, who chairs the Exiting the European Union Committee, the SNP’s Angus B MacNeil, of the International Trade Committee, and the Science and Technology Committee’s Lib Dem chair Norman Lamb among others.

The government lost a vote in the Lords on Wednesday, which pushes Ms May to take steps towards negotiating for the UK to stay in a customs union after Brexit.

Ministers and even some rebels believe the motion is not strongly worded enough to force the government’s hand, and Ms May is likely not to try to overturn it in the Commons.

But rebels say it does act as a signpost for the direction of travel on where the government should be heading in Brexit negotiations, with next week’s vote serving a similar purpose, and showing ministers that the Commons and Lords are both behind the idea of a post-Brexit customs union.

Dominic Grieve tables amendment seeking to stay in customs union

Later in the year, the government will have to face votes on two rebel amendments tabled to pieces of Brexit legislation, calling for the UK to remain in a customs union, which will be binding.

Rebels have said the earlier non-binding votes should serve as reminders to the government, before it gets to the binding ones, that it faces strong opposition to taking the country out of any customs union with Europe.