Theresa May’s Brexit plan will be blocked by MPs even if she is able to “bounce” the Cabinet into signing it off, the Prime Minister has been warned.

Senior members of the Eurosceptic grouping of Tory backbenchers and the Democratic Unionist Party figures are publicly uniting to insist they will vote against Mrs May’s proposals unless she backs down.

Their intervention came as senior government figures warned that the deal would still fall in Parliament even if it were forced through a reluctant Cabinet this week. A defeat for Mrs May would be likely to spark a leadership challenge.

The warnings come amid opposition from across the Conservative Party to a proposed “backstop”, or insurance plan, for the UK’s relationship with the EU if no alternative deal is reached.

Ministers and MPs are concerned it could allow for a border between Northern Ireland and the rest of the UK, and would provide an insufficient mechanism for the country to extract itself from the EU’s structures.

The plan sparked the resignation of Jo Johnson, the pro-Remain transport minister, on Friday, on the basis it amounted to “vassalage” for the UK.

Around 10 Cabinet ministers have rejected the idea of an exit mechanism from the backstop that depends on the EU giving its permission for the UK to leave its structures, leading to speculation some may resign. But a senior Tory claimed the ministers would ultimately “fall like paper tigers” – referring to a Chinese expression about objects that appear threatening but are ineffectual.