British Prime Minister Theresa May promised to deliver a "successful" exit from the European Union, strengthen Britain's economy and build a "fairer society for everyone" in a New Year's message on Sunday.

May said 2017 had been a "year of progress" for Britain, in which she had triggered two years of formal Brexit negotiations in March.

Whether people voted for or against Brexit in the referendum in June 2016, "most people just want the government to get on and deliver a good Brexit, and that's exactly what we are doing," she said.

"Making a success of Brexit is crucial, but it will not be the limit of our ambitions.

"We also have to carry on making a difference here and now on the issues that matter to people's daily lives," May said.

She promised "a balanced approach to government spending, so we get our debt falling but can also invest in the things that matter - our schools, our police and our precious NHS [National Health Service]."

"I believe 2018 can be a year of renewed confidence and pride in our country," May said.

"A year in which we continue to make good progress towards a successful Brexit deal, an economy that's fit for the future, and a stronger and fairer society for everyone."

Opposition Labour leader Jeremy Corbyn said his party wanted to "show how the old political consensus is finished" in Britain in 2018 by building on its surprisingly strong performance in a snap election in June.

Speaking to the pro-Labour Daily Mirror newspaper, Corbyn said he wanted to put Labour "at the heart of every community," particularly post-industrial communities that have been "failed by economic changes over the last 40 years."

Liberal Democrat leader Vince Cable said his party "will continue to stand up for our values" in the new year.

"We will offer people the choice of an exit from Brexit," Cable said, referring to the Liberal Democrats' campaign for a second referendum on whether Brexit should go ahead.

In an earlier message, Foreign Secretary Boris Johnson said he planned to focus on efforts to curb the global trade in ivory next year.

"Our great-grandchildren deserve to share the planet with wild elephants, which is why I will make 2018 the year of British leadership in defeating the ivory trade," Johnson said on Twitter.

Writing in The Times, he said he had ordered British diplomats worldwide to hold "frank conversations with our friends and allies" on the ivory trade.

"The slow death of Africa's elephants is a disaster that proceeds from other disasters," Johnson wrote.