LONDON (Reuters) - A lawmaker from the small Northern Irish party that British Prime Minister Theresa May’s government relies on for support has said his party will not be bullied in Brexit talks, and that an unacceptable deal will be defeated in parliament.

Writing in the Telegraph, Democratic Unionist Party (DUP) lawmaker Sammy Wilson said May’s British government should not blink in negotiations and would face the consequences if it submitted to “draconian” proposals from the European Union that could keep Britain tied to its customs union.

“If the Government decides in the face of EU belligerence to cut and run and leave part of the UK languishing in the stifling embrace of the EU, then that would be totally unacceptable to us and many others in the House of Commons,” Wilson said, warning of parliamentary defeat for any deal that crossed his party’s red lines.

“We will not be bullied into propping up a soft-touch Government which gives in to the EU’s demands.”

Earlier, the EU’s chief negotiator, Michel Barnier, said Britain must accept possible checks on goods moving between its mainland and its province of Northern Ireland, saying Brexit would trigger the need for customs, value-added tax and compliance checks with EU standards.

Barnier said he realized such checks were politically difficult but this was the consequence of Britons voting to leave the EU.

Britain has agreed a need for a “backstop” deal on the Irish border in case a future trading arrangement is not finalised.

But Wilson said reports of a Brexit deal involving either the UK staying within the customs union for an unspecified time-limited period or an arrangement that excluded Northern Ireland from any trade arrangements that the UK made with other countries in the future would be unacceptable.

He also said that the party would oppose the government if the deal involved EU regulations being applied to goods and services produced in Northern Ireland and checks on movements of goods from Great Britain to Northern Ireland.

The BBC and Sky News have reported that the DUP is considering voting down the government’s budget next month if it crosses the party’s red lines on Brexit.

“If the Government is putting these proposals into the public domain to test the water, our advice is to get its toe out quickly or it is going to get burnt,” Wilson wrote.