Britain will be the first member state ever to leave the bloc.
Asked if he was now accepting Brussels' timetable, as set out by chief negotiator Michel Barnier, Mr Davis said: "What we have said is we will start down this process but I will have some discussions with Mr Barnier about how we progress to the wider thing of the trade area". Contrary to expectations, the snap general election in the United Kingdom has thrown up a hung Parliament with the Tories emerging as the largest party, but falling short of a majority.
May gambled that a strong election win, as forecast by some pollsters, would boost her majority in the House of Commons in time for the Brexit talks, but instead, her party surrendered 13 seats in the lower chamber.
"Our view is that withdrawal agreement and terms of the future relationship must be agreed alongside each other", said the spokesman.
But the Government signalled it will continue to push back against the Commission's stance by declaring the UK's withdrawal and future relationship with the European Union are "intimately linked".
He added: "As the European Union has itself said, "nothing is agreed, until everything is agreed".
Mr Davis added: "In the first round we are going to have pretty long meetings at roughly one week a month - which is much, much faster than any previous trade deal they have done".
Chancellor Philip Hammond said the Government's priority in the negotiations should be to protect jobs, economic growth and prosperity.
The UK Government wants the talks to take place in parallel during the Brexit process.
"My clear view, and I believe the view of the majority of people in Britain, is that we should prioritize protecting jobs, protecting economic growth, protecting prosperity as we enter those negotiations", Hammond told reporters before a meeting of the 28 European Union finance ministers in Luxembourg.
The Chancellor had been due to use a high-profile speech in the City of London on Thursday night to send out a message the Government would protect business from shocks during the Brexit process.