Theresa May’s new year message urging unity and pledging to also represent the interests of remainers during negotiations with Brussels are empty words given her previous hardline approach, the Liberal Democrat leader, Tim Farron, has said.

In her video message May acknowledged how divisive June’s referendum had been and said both sides would be in her mind as she prepared to trigger article 50.

“I am there to get the right deal not just for those who voted to leave, but for every single person in this country,” she said, counter to recent hints that the government is preparing a hard Brexit, which would see the country leave both the customs union and the single market.

Farron, whose party is campaigning for a second referendum on any exit deal finalised with the EU, said: “After months of platitudes and driving us headlong towards a hard Brexit out of the single market, threatening jobs and our economic security, a few empty words are utterly meaningless.

“If the prime minister cannot even deliver on the words she gave when she campaigned for remain, why should we believe her now? In all of this she has Labour holding her hand, marching towards a disastrous Brexit.”

In recent days, leave campaigners have stepped up efforts to push for what they term a “clean break’ with Brussels, with the UK cutting all formal ties with the bloc.

In a letter sent to the prime minister, the pressure group Leave Means Leave said leaving the single market and the customs union should be “red lines” for the prime minister.

“There must be no transitional deal on the key issues,” the group’s co-chairs Richard Tice and John Longworth wrote. “The EU is renowned for its inability to secure trade deals within a sensible timeframe and the UK must be prepared to walk away and secure trade deals with the rest of the world if the EU fails to agree a deal in this timeframe.”