Johnson had previously said he would rather be "dead in a ditch" than ask for any extension to the Oct. 31 deadline.
As a poll for the Observer newspaper indicated growing dissatisfaction with Johnson's handling of the crisis, he wrote in the Mail on Sunday paper: "I understand that people will feel frustrated with some of the new rules."
Having taken over a minority administration in July and unable to speed his EU divorce deal through parliament, Johnson is seeking a majority at the December 12 snap general election.
More than 4,000 polling venues across England, Scotland, Wales and Northern Ireland, including a windmill, several pubs, a hair salon and a chip shop, opened their doors for a day of voting that ends at 2200 GMT.
Britain’s main opposition leader Jeremy Corbyn apologised Sunday for waging a disastrous campaign that handed Prime Minister Boris Johnson a mandate to take the UK out of the EU next month.
European Union members agreed Monday to postpone Brexit for up to three months, stepping in with their decision less than 90 hours before Britain was due to crash out with no divorce deal.
The 358 to 234 vote paves the way for Prime Minister Boris Johnson to deliver on his winning general election promise to "get Brexit done" by January 31.
We all have to improvise in these unusual times. That applies to the Peter Mandelson Memorial Dim Sum Supper just as much as to any other venerable institution of the unwritten British constitution. One of the great strengths of the constitution
UK Prime Minister Boris Johnson has previously described himself as a “son-in-law of India”, owing to his former wife’s Indian mother. According to reports, he is a self-proclaimed Indophile.