With the Cabinet’s Brexit sub-committee due to meet on Wednesday and Thursday to thrash out the final negotiating position, Ms Rudd made it clear that they will push for the power to make independent trade deals.
The Home Secretary was commenting following criticism by a senior Tory backbencher and Brexit supporter Bernard Jenkin that ministers are “vague and divided” on a strategy.
He also voiced new concerns about Chancellor Philip Hammond and suggestions that the Treasury is trying to reverse government policy and keep Britain under Brussels rule in the EU customs union.
If this happens the UK will not be free to make trade deals and will have to accept dictats from the EU.
“She can only command a majority in Parliament on her present policy. Nearly half David Cameron’s MPs, voted Leave, despite his patronage and pleadings. There would have been few Remain Tories if he had advocated Leave,” Mr Jenkin wrote.
“Her MPs will back her, because we are overwhelmingly at one with the majority of the British people who now want a clean Brexit and an end to the present uncertainty.
“It is time for all her ministers to back her too and to end the confusion they are fomenting in government.”
His concerns followed claims by Jacob Rees Mogg that Treasury civil servants are trying “fiddle the figures” to undermine Brexit.
Ms Rudd said ministers were committed to getting a deal which would enable Britain to strike free trade deals with other countries while maintaining “frictionless” trade with the EU.
“I have a surprise for the Brexiteers, which is the committee that meets in order to help make these decisions is more united than they think,” she told BBC1’s The Andrew Marr Show.
“We meet in the committee. We meet privately for discussions. I think that we will arrive at something which suits us all.
“There will be choices to be made within that, but we all want the same thing which is to arrive at a deal which works for the UK.”
Ms Rudd acknowledged that it would probably involve some form of customs “arrangement” or “partnership” with the EU, but said the Prime Minister had an “open mind” as to how that could be achieved.
“We a want frictionless trade at the border, we want to make sure that there is no border on the island of Ireland and we want to make sure that we can do trade deals outside of the European Union. That is the deal we are looking for,” she said.
“We need to have this wider agreement. I don’t know how far that will go over the next few weeks but I hope the Government will be give the space to try and achieve that.”