British Prime Minister Theresa May has said that her government is "proving the doubters wrong" after European Union leaders agreed that Brexit negotiations can finally move on to their next phase in the new year.

Leaders of the other 27 EU nations gave a boost to May on Friday when they declared that talks over Britain's exit can proceed to the issues of transition and future relations.

Writing in two Sunday newspapers, May also struck a defiant note and said her Brexit plans won't be "derailed" by anti-Brexit campaigners.

May, who is already struggling to maintain her authority amid the fractious exit process, suffered a significant political defeat in Parliament on Wednesday when the House of Commons voted to give lawmakers the final say on any Brexit agreement.