He said his goal is an ordinary withdrawal and that he will circulate draft guidelines for the EU's negotiating stance on Friday.
Former UK Independent Party leader Nigel Farage tweeted: "The impossible dream is happening. Today we pass the point of no return."
The dust will take a while to settle as the Brexit debate continues, with little sign that May's plea for unity had been heeded.
Pro-remain organizations and individuals continued to fight their corner. Outside the British Parliament, dozens of protesters against Breixt were waving signs, shouting slogans and singing "Ode to Joy," the anthem of both the Council of Europe and the European Union.
In London, where nearly 300 international banks have branches, a sense of uncertainty could be easily felt.
Cremeut Labit, a French national working in the financial quartet of London, told Xinhua he felt regretful about Brexit. "There is going to be a period of uncertainty," he said. "We need to be cautious before taking every step."
Jonathan Warburton, a London-based banker working for a French bank who takes the Eurostar every other week, thinks Brexit will not affect his travel unduly. "The bank might shift about 5 percent of its staff over, but London is the hub, and where the talent is," he told Xinhua.
Musician Lewis Fieldhouse, 28, born in the year the Berlin Wall fell, said: "I have never feared boots on the ground like earlier generations, so I regret us leaving."
LENGTHY, TOUGH TALKS
A new UK-Europe relationship is expected to emerge after the Brexit negotiations which are doomed to be lengthy and tough.
Observers have predicted that Britain and Europe will differ on a wide range of issues, including immigration control, free-trade agreement and a multi-billion-pound exit fee.
The full effects of Brexit on Britain's trade relations may not be resolved in a further two decades, British economist and writer Martin Wolf told Xinhua.
In an assessment of the complex road ahead for Britain as it creates new economic and trade ties, Wolf warned that exit from the EU was merely the first step on the journey.
"We will be making up a new trade policy which will probably take us 20 years," said Wolf, who is the associate editor of the London-based daily newspaper the Financial Times and also its chief economics commentator.
Matthew Elliott, one of the leading forces behind the successful Brexit campaign told Xinhua in a recent interview: "Brexit means leaving the single market and leaving the customs union," which he described as "a full one."
