Housing Minister Richard Harrington wrote a memo claiming the plan had already been rejected. Senior EU figures are currently refusing to renegotiate the backstop. Chief Brussels negotiator Michel Barnier claimed it was “part and parcel” of the deal.
Mr Harrington hit out at Mrs May’s plans in a memo leaked to The Daily Telegraph.
Referring to the customs union he wrote: “This idea was considered and rejected by both the UK and the EU in summer 2018, as both parties concluded that it would not maintain an open border.
“That is why we ended up with the current backstop.
“There is currently no border in the world, outside a customs union, which has eliminated border infrastructure.”
Separately a Cabinet Minister said Mrs May’s plan is “insane, it is mad because we are trying to renegotiate our own deal”.
Mrs May is seeking concessions to allow her Brexit deal, rejected earlier this month by a record margin, to pass Parliament.
The House of Commons voted it down on January 15 by a margin of 230 MPs.
Under the terms of the backstop, designed to stop a hard Northern Irish border, the UK will automatically drop into a customs union with the EU if a new trading relationship can’t be agreed during the 21-month transition period.
The UK would then struggle to leave this customs union without express permission from Brussels.
There are also reports Oliver Robbins, the Prime Minister’s chief Brexit negotiator, warned against reopening backstop negotiations with the EU.
He argued the EU would not make significant legal changes to the backstop.
A source said: “The gist of the email was that it wasn’t worth the paper it’s written on.”
Parliament approved Mrs May’s plan to renegotiate the backstop by 317 votes to 301 on Tuesday night.