The Prime Minister made the vow despite the EU insisting regulatory alignment was a requirement for any future relationship. Friday saw Mr Johnson's Brexit deal pass through Parliament with a majority of 124. Speaking in the Commons chamber the PM said it "means we are one step closer to getting Brexit done.".
The bill was backed by six MPs from the Labour Party - Sarah Champion, Rosie Cooper, Jon Cruddas, Emma Lewell-Buck, Grahame Morris and Toby Perkins.
32 MPs from the Labour Party abstained whilst 162 Labour MPs joined 45 SNP MPs, all 11 Liberal Democrats, 7 DUP MPs and all 4 Plaid Cymru MPs in voting against.
353 Tory MPs joined the 6 Labour rebels in voting for the deal.
Mr Johnson told MPs to "move on" from Brexit and "disregard the old labels of Leave and Remain".
Boris Johnson has vowed there will be no regulatory alignment with the EU post Brexit
Leo Varadkar has said the development made a trade deal harder to achieve
He said the result of the vote “paves the path for a new agreement on our future relationship with our European neighbours based on an ambitious free-trade agreement, with no alignment on EU rules, but instead control of our own laws and close and friendly relations”.
Irish Taoiseach Leo Varadkar said: “We don’t want to trade with a Britain that undercuts us, that has lower financial standards, lower product standards, lower health and safety standards, the harder approach being taken by Prime Minister Johnson is a risk to us.”
European Council President Charles Michel said: “A level playing field remains a must for any future relationship.”
Trade talks with the EU can only officially begin when Brexit takes affect at the end of next month.
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Charles Michel is European Council President
An EU source said that instead of getting a "Canada-plus" trade deal, Mr Johnson would end up with little more than a "WTO-plus" deal, which means tariffs may be involved.
Brussels had hoped Mr Johnson's majority in last week's election would allow him to ignore the harder Brexiteers within the party.
A senior diplomat from the EU told the Telegraph: “The more Britain will diverge from common standards and regulations, the more time we will need to negotiate a comprehensive trade deal.
"Due to the 11-month time limit imposed by London, the risk of a cliff edge by the end of 2020 has risen considerably.”
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Stephen Barclay is Brexit Secretary
Sarah Champion was one of six Labour MPs to vote for Mr Johnson's withdrawal agreement
A senior Government source responded: “EU officials claimed that they wouldn’t reopen the Withdrawal Agreement, but they did as it was plainly in our shared interest.
“There is clearly political will on both sides that will ensure we can conclude an ambitious free trade agreement by the end of next year.”
Mr Johnson will be in the EU over the Christmas period as he serves Christmas lunch to British Armed Forces personnel serving with NATO in Estonia.
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January 31 will also see the closure of the Department for Exiting the European Union.
A statement from No 10 thanked staff for their work and and said they will be helped to find new roles.
The department is headed by Brexit Secretary Stephen Barclay.
Theresa May's withdrawal agreement was rejected three times
The Lord Callanan is the Brexit Minister whilst James Duddridge is the Parliamentary Under-Secretary of State.
David Davis was the first Brexit Secretary but resigned in 2018 over the Chequers Agreement which detailed the Theresa May government's plans for a future relationship, Mr Johnson resigned as Foreign Secretary at the same time.
Mr Davis was replaced by current Foreign Secretary Dominic Raab but he too resigned after just four months over his opposition to the withdrawal agreement agreed by Mrs May.