British Prime Minister Boris Johnson has won approval for his Brexit deal in parliament, the first step towards fulfilling his election pledge to deliver Britain's departure from the European Union by 31 January after his landslide victory.

MPs voted by 358 to 234 pass the second reading of the legislation, underlining Mr Johnson's large majority in parliament that should ensure a smooth ratification of the divorce deal to implement Britain's biggest policy shift in more than 40 years.

More than three years since Britain voted to exit the EU in a 2016 referendum, the deep uncertainty over Brexit has now been replaced by the firm deadline of the end of January.

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Only after that will the prime minister face talks to secure a trade deal with the bloc and another target date of the end of next year.

Getting "the Brexit vote wrapped up for Christmas" was the main aim for Mr Johnson showing that, unlike his predecessor Theresa May, he now had free reign to drive Brexit forward despite continued criticism from opposition MPs.

"This is the time when we move on and discard the old labels of 'leave' and 'remain' ... now is the time to act together as one reinvigorated nation, one United Kingdom," Mr Johnson told parliament before the vote.

Read more: Harder Brexit approach a risk to Ireland - Varadkar

"Now is the moment to come together and write a new and exciting chapter in our national story, to forge a new partnership with our European friends, to stand tall in the world, to begin the healing for which the whole people of this country yearn."

The final stages of ratification will take place after Christmas, with the House of Commons having until 9 January to approve the legislation, or Withdrawal Agreement Bill, giving it just over three weeks to then pass through the House of Lords and receive royal assent.

Labour leader Jeremy Corbyn labelled the government's handling of Brexit as a "national embarrassment" since 2016, as he said his party "recognises the clear message" from voters at the election but confirmed Labour would not support the bill.

He said Mr Johnson was offering a "terrible" Brexit deal, adding: "Labour will not support this bill as we remain certain there is a better and fairer way for this country to leave the European Union.

"One which would not risk ripping our communities apart, selling out our public services or sacrificing hundreds of thousands of jobs in the process.

"This deal is a road map for the reckless direction in which the government and our Prime Minister are determined to take our country," said Mr Corbyn.

The Taoiseach has said a harder than anticipated approach to Brexit by Mr Johnson is a risk to Ireland.

Speaking at a press conference in Dublin, Leo Varadkar said that while a lot has been achieved in the Withdrawal Agreement, he remains concerned about Brexit because the question of trade is still open.