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But the turmoil of the euro zone crisis, fears in Britain about immigration and a series of miscalculations by former Prime Minister David Cameron prompted Britain to vote by 52 to 48 percent for Brexit in a June 23 referendum a year ago.
The government's plan for the next Parliament will be outlined in the Queen's speech on Wednesday, and will include laws needed to deliver Brexit and new immigration legislation.
The government is due to present its legislative programme at the opening of parliament on Wednesday, which will be followed by a key confidence vote several days later.
Compounding the pressures on the British leader, she has been widely accused of failing to show enough empathy with victims of a horrific tower block fire in London last week.
Opponents of Brexit fear that ditching a 60-year strategy of trying to hedge European integration with a special relationship with Washington or a brittle Commonwealth of former colonies would undermine what remains of Britain's global influence.
Asked whether Britain could stay inside the customs union, Sir Keir said: 'Yes'. "My role in the election campaign was not the one I would have liked it to be", he said, arguing that the Conservatives should have talked more about their economic record.
While "Brexiteers" have strongly backed Mrs May's proposed clean break with the single market and customs union, finance minister Philip Hammond and others have this month echoed calls by businesses for less of a "hard Brexit" and retaining closer customs ties.
Other view: Scalise shooting: Playing congressional baseball game shows needed unity
The 59th annual baseball game, played at Nationals Park in southeast Washington , looks to be a place where members can show it. Democratic former Alexandria Mayor Bill Euille said he had spoken often with the man on recent mornings at the nearby YMCA.
Andrea Leadsom, leader of Britain's lower legislative house, said that Brexit would require a lot of legislation, including a law to enshrine current European Union rules into British law, known as the "Great Repeal Bill".
But Hammond said transitional arrangements would be necessary, to give business greater certainty.
"It's a statement of common sense that if we are going to radically change the way we work together, we need to get there via a slope, not a cliff edge", he said.
The start of the negotiations comes as work continues across the British government to prepare Britain for life outside of the EU.
However, Europe says that an agreement on issues such as the rights of citizens, the divorce bill and border controls must come before considering any post-Brexit settlement.
As has been the case throughout the run-up to the official talks, the main emphasis of the preview was on the U.K.'s desire to secure a future relationship with the EU.
A year after the referendum, he has travelled to Brussels for the opening of negotiations.
The chancellor said he would reject any deal "designed to destroy us".
International Trade Minister Liam Fox will travel to Washington on Monday to explore new trade ties - although no formal negotiations are possible until Britain has actually left the bloc. 53% of people said that there should be a second vote on Brexit.