"So in that sense from the day the Mansion House speech was delivered [when the prime minister set out plans for the UK's future relationship with the European Union on 2 March] we've been thinking about how we deliver it and how to make sure the negotiation position we advance with the European Union is sufficiently precise to achieve our objectives".
Overall responsibility for the talks is being moved to the Cabinet Office, the ministry which supports May and where her main Brexit advisor, civil servant Olly Robbins, is based.
Downing Street confirmed that it will be Mr Raab who travels regularly to Brussels for direct talks with European Union chief negotiator Michel Barnier.
Asked about European Commission comments that there were no arrangements in place for United Kingdom and EU expats in the event of no deal, Mr. Raab said: "Well, I think that's a rather irresponsible thing to be coming from the other side".
A shift in responsibility has been under way for months, as Davis was increasingly sidelined by Robbins before he quit - in what one eurosceptic MP suggested on Tuesday was a "coup d'état".
He said that while he was confident the United Kingdom and European Union would strike a compromise deal, it was "the responsible thing to do to be prepared" in case no agreement is reached.
The two sides want to strike an initial withdrawal agreement by late October, in order to give parliament enough time to endorse it, before reaching a broader deal on their future relationship.
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Also in the session, Robbins revealed that teams from the Cabinet Office Europe Unit as well as from the Treasury, the Department for Business, Energy and Industrial Strategy, and the Department for International Trade, have been working together to achieve "as frictionless trade as possible between the United Kingdom and the European Union".
Only 16% of voters support Theresa May and consider she is doing well with Brexit compared to 34%, according to which Johnson will do a better job.
May was also set to make use of the opportunity to defend the Brexit proposals that have not gone down well with her Conservative supporters and the general public.
But he said the plan was a "road map" to the "sunlit uplands" of a final deal which respects the referendum result.
Raab met the EU's top negotiator Michel Barnier for the first time on Friday, where he heard doubts over May's new Brexit blueprint for the future relationship.
Britain will publish around 70 "technical notices" in August and September setting out what citizens and businesses would need to do.
Raab told the same committee that he and Robbins had been working "very closely together from day one to make sure there is one team".