Conservative rebels have warned they have the support of growing numbers of MPs in a bid to force Theresa May to keep Britain in a customs union with the EU.

Former cabinet minister Dominic Grieve said he believed a “broad swathe of the Conservative party in Parliament” backed a proposed amendment to Ms May’s trade bill that would secure the change in government position.

Increasing numbers of Conservatives and Labour MPs were signing up to the proposal on Friday, with prominent Tory Remainer Anna Soubry among their number claiming there would be “many others”.

It comes as Labour leader Jeremy Corbyn plans to make a Brexit speech on Monday in which he is also expected to signal backing for staying in a customs union, leaving major questions over whether Ms May can maintain her opposition to one.

Speaking on the BBC’s Daily Politics, Mr Grieve said: “My view has always been that the national interest lies in our maintaining [tariff free trade] and, if that means being in a form of customs union, then I don’t think that’s something that we ought to rule out.”

The former Attorney General added: “If the Government were defeated eventually on this, then the Government would, I would assume, be required to keep us, or seek to negotiate keeping us, in a customs union if that of course can be obtained from our EU partners.”

The next stage of the trade bill has been delayed until after April, in large part because government whips are attempting to manage the rebellion over the customs union.

David Davis tries to dispel post-Brexit chaos fears

If passed, the amendment would make it an “objective of an appropriate authority to take all necessary steps to implement an international trade agreement which enables the UK to participate after exit day in a customs union with the EU in the same terms as existed before exit day”.

Labour MP Chuka Umunna, who also signed the amendment, said: “Parliament is in the driving seat, and there is a majority to continue participating in a customs union with the EU.”

A string of Labour frontbenchers have indicated that their party is moving towards backing maintaining the UK in a customs unions with Europe, with Jeremy Corbyn set to deliver a keynote speech on the issue after the weekend.