The divisions among senior Tories over Brexit were laid bare on Sunday as government ministers contradicted each other on vital details within minutes.

Amber Rudd, the Home Secretary, and Dominic Raab, the housing minister, offered drastically different predictions of the UK’s future relationship with the European Union.

Ms Rudd said the UK should remain in some form of customs arrangement with the bloc – a view she suggested was shared by Theresa May. However, Mr Raab, a Brexiteer, said he did not think Britain would be part of any kind of customs union after Brexit.

The divisions come ahead of two crucial meetings of the Cabinet’s Brexit sub-committee this week, at which warring ministers will attempt to thrash out a common position on the UK’s future relationship with the EU single market and customs union.

The Government has said it wants to maintain “frictionless trade” with the EU – an aim widely thought to require some form of customs agreement.

Ms Rudd told the BBC’s Andrew Marr Show: “We published a document last year and we proposed either a customs arrangement or a customs partnership. Those are both alternatives we could look at.

“We do not want to have tariffs at the border, so that is a form of customs agreement, arrangement [or] partnership. It is likely to be something within the customs framework.”

In a warning to her cabinet colleagues insisting the UK should leave the customs union, she added: “If you set up trade barriers, there is a consequence to a trading nation.

“I am very enthusiastic for making sure we have as few trade barriers as possible. The Prime Minister has said she wants frictionless trade at the border and that’s what we need to achieve. If we put up trade barriers, it won’t help our economy.”

However, minutes later, Mr Raab told Sky News’s Paterson on Sunday: “I don’t think we’ll be in any form of customs union, at least as conceived in international trade practice.

“Because if we were we would have our hands tied in negotiating free trade deals with other parts of the world, whether it’s Brazil, whether it’s China or India. The Prime Minister has been very clear we want to be able to grasp those opportunities.”

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Theresa May has previously said she has “an open mind” on the issue. She will this week attempt to find a middle ground between senior ministers who have very different views on the UK’s future relationship with the EU.

Leading Brexiteers Boris Johnson, Liam Fox and Michael Gove are set to strongly resist plans for any kind of customs union. That places them firmly on a collision course with cabinet colleagues Ms Rudd, Philip Hammond and Greg Clark, who believe any move towards imposing tariffs would harm the economy.

Reports suggest Mr Fox could resign if he does not get his way. The International Trade Secretary said last week that it was “very difficult to see how being in a customs union is compatible with having an independent trade policy”.

Tory Eurosceptics are also thought to be considering a coup to replace Theresa May with Mr Johnson, assisted by Mr Gove as his deputy and Jacob Rees-Mogg, a leading backbench Brexiteer, as Chancellor.

Ms Rudd, however, said she was confident a deal would be reached.

She said: “I have a surprise for the Brexiteers, which is that the committee that meets in order to help make these decisions is more united than they think. We meet in the committee, we meet privately for discussions and I think we will arrive at something which suits us all.”

She was "not intimidated" by the Eurosceptics' demands, she added.

Jacob Rees-Mogg claims civil servants are 'fiddling figures' on Brexit

But in a further sign of widening Tory divisions over Brexit, the Home Secretary criticised Mr Rees-Mogg, chair of the influential European Research Group of Eurosceptic Tory MPs, for suggesting civil servants are “fiddling the figures” to influence policy in favour of a softer withdrawal from the EU.

Mr Rees-Mogg claimed on Saturday that Treasury officials were “running policy that is not government policy” and has previously alleged the department “deliberately” skewed an analysis document.

Asked about the allegations and the integrity of civil servants, Ms Rudd said: “I have complete confidence in them. We are envied the world over for the high standards of our civil servants.”

She added: “I’m very surprised at Jacob because he is famously courteous, famously thoughtful and articulate, so I’m very surprised that he’s used this language. I think that he is wrong.