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Senior Conservatives in Cabinet and on the backbenches are drawing up a “customs union in all but name” in a bid to force an end to a major split over Brexit policy.

The move emerged as Downing Street rushed to deny reports that it was threatening to turn a Commons vote on the issue into a form of “confidence vote” that would end Theresa May’s leadership or even topple the Government if she lost.

The Evening Standard has learned that a confidential group of ministers and former ministers are designing proposals that could be accepted by both sides as a fair compromise.

It could involve the UK accepting most of the rules in future but being free to negotiate trade deals in industrial sectors and with countries that are not covered by EU agreements.

The disclosure comes ahead of a series of dramatic Commons votes that are likely to show Mrs May does not have a big enough majority to steamroll a hard Brexit through Parliament.

On Thursday some 10 Conservatives including former ministers Nicky Morgan and Anna Soubry will vote alongside Labour on a motion instructing the Government to “take all necessary steps” to “participate after exit day in a customs union”.

A binding amendment to a trade Bill next month is seen as a more critical showdown that would tie the Prime Minister’s hands to a form of customs union if she loses.

A No 10 source denied that Mrs May was looking for a compromise saying the only options being studied were the two plans set out by the Government last year; one is for a frictionless border and the other is for a partnership in which the UK would collect levies on goods heading for the EU market.

“These are the only models we are looking at,” said the source.

Dismissing a BBC report that a confidence vote was being considered, the source said: “Everybody needs to calm the f*** down.” But a senior minister said he believed Mrs May was moving towards a compromise with the rebels. “We are most likely to end up with a customs union in all but name which would be backed by a good majority of the House of Commons,” he said.

A minister who supports Mrs May said “soft Brexiters” led by former Chancellor Kenneth Clarke had signalled their own willingness to compromise if a deal is found. “Ken Clarke has used language that suggests he is not hidebound to a customs union arrangement if the benefits can be obtained by another means,” said the minister.

Among the group that is drafting a potential compromise is Dominic Grieve, the former Attorney General. A source said: “There are discussions taking place with colleagues inside and outside of Government.”

Mayor Sadiq Khan called on London’s EU nationals to use next week’s local elections to protest against Brexit. Speaking in Wandsworth, he said: “We need to send the Tory Government a clear message that we don’t want their extreme and irresponsible approach to Brexit.”