Britain who experienced bitter divisions after the June referendum, in which 52 percent of people voted for the country to exit the EU.
May, who succeeded David Cameron as prime minister after the Brexit vote, said in her message that "coming together is also important for us as a country."
"As we leave the European Union we must seize an historic opportunity to forge a bold new role for ourselves in the world and to unite our country as we move forward into the future," May said in her first Christmas message as prime minister.
The Supreme Court is set to rule in January on whether the British parliament's approval is needed for May to trigger the exit process.
the PM wants to start formal
Brexit negotiations with the EU by the end of March. The process would then take two years to complete.
But the premier hasn't revealed much about how she intends to carry forward her Brexit plan, saying it would be foolish to show her cards before the start of negotiations with the EU.
"It is absolutely right that we do not set out at this stage every single detail of our proposed negotiating strategy, because that would be the best way to get the worst possible deal for Britain," May told parliament when asked whether she had a coherent plan.
British media reported that the Queen was "disappointed" by May's refusal to share Brexit plans with her in private talks between the two.
Sometime this week, the Scottish government unveiled their plans to stay within the EU single market after the UK triggers Brexit. Prime Minister May criticized the Scottish proposal and said some of the proposed measures might be "impractical."