Ukip's interim leader has warned Theresa May that it would be "absolutely unacceptable" to water down her Brexit objectives following the General Election result.
The Prime Minister lost her majority and Ukip lost its leader in a disastrous General Election for both parties.
Steve Crowther, who is standing in as Ukip leader following Paul Nuttall's resignation, said an end to freedom of movement must be secured in the Brexit talks.
Mrs May hopes to run a minority government with the support of the DUP's 10 MPs.
Mr Crowther said: "Though she is personally damaged as our negotiator, the suggestion that Mrs May's dismal electoral performance relieves the Government of the need to achieve full Brexit is absolutely unacceptable.
"The people voted last year to leave the EU, full stop. Mrs May's incompetent electioneering makes not the slightest difference to that. If the Conservative-DUP government thinks it can backslide on this, it will rapidly find that it is mistaken.
"In particular, the DUP's concerns about the Irish border issue must not lead to an acceptance of any 'free movement of people' in the negotiation. The Common Travel Area provisions in place since the 1920s are a perfectly adequate basis for resolving that anomaly.
"The people of this country want control of their borders and an end to the disastrous policy of open-door immigration which has led to a rapidly-rising population, a funding crisis in health and education, pressure on housing and wages, and dangerous social alienation."
Mr Nuttall quit after finishing a distant third in his bid to win a Commons seat in Boston and Skegness as the Ukip vote share collapsed nationally.