Current Brexit Secretary Dominic Raab meanwhile lashed out at Brussels accusing it of being irresponsible for "flagging up" risks to European Union nationals living in the United Kingdom from a no-deal Brexit, the Guardian report said.
The pair presented a united front, with Mr Raab insisting there was "no tension" between him and Mr Robbins despite "some shifting of the Whitehall deckchairs".
Raab only took up the role on 9 July, after his predecessor David Davis quit in protest at May's plan for close economic ties with the EU.
The risks of not reaching a Brexit deal were underlined by Cabinet ministers on Tuesday. "I will be deputising for the Prime Minister in the negotiations".
May, however, said "DExEU will continue to lead on all of the government's preparations for Brexit", preparations that will include both a deal and a no-deal scenario.
Officials working on the negotiations will be brought together in the Cabinet Office Europe Unit headed by Mr Robbins - who reports direct to the Prime Minister - while Mr Raab's Department for Exiting the European Union will focus on preparations for life after Brexit.
According to a report from the Financial Times, the EU's chief negotiator Michel Barnier, last Friday told European Union ministers that the financial services elements of May's Brexit plans could not be accepted as they threatened to rob the bloc's "decision-making autonomy" when it comes to finance.
The prime minister added Mr Raab's DExEU officials will now exclusively focus on Brexit preparations, including those for a "no deal" outcome.
There will be no net reduction to staff numbers in Mr Raab's department, she said.
The main opposition Labour Party responded to the announcement with shadow Brexit minister Jenny Chapman saying May's newly appointed Brexit Secretary Dominic Raab had been sidelined.
Leave Means Leave co-chair Richard Tice said that Mr Raab and DExEU had been "completely undermined".
Prime Minister Theresa May says the North east and Britain will prosper after Brexit.
"The Prime Minister has made yet another catastrophic error and has lost the trust of majority of the British people".
James Rossiter, Senior Global Strategist at TD Securities, points out that the last few weeks have been tumultuous ones for Brexit negotiations as expectations have swung, in the span of just days, from a soft Brexit (in the wake of Chequers) to a hard one (following amendments to the Customs Bill).
As Mr Raab and Mr Robbins appeared in front of the Exiting the EU Select Committee, Eurosceptic Tory Craig Mackinlay suggested there had been a civil service "coup d'etat", while fellow Brexiteer Peter Bone suggested Mr Robbins had been responsible for a "secret" plan which led to the Chequers proposals.
May's controversial white paper dismissed the asset management industry's favoured mutual regulatory recognition model in favour of an enhanced version of the "equivalence" model, which enabled the likes of the USA and Singapore to simplify their access the bloc.
It has been more than two years since the referendum, and I know many people want us to get on and deliver on the verdict of the British people.