A senior Democratic Unionist Party (DUP) figure told CNBC Tuesday that politicians in Brussels would clamour for fresh terms of trade with the U.K. should the country leave the European Union with no deal.

Sammy Wilson, the Brexit spokesman for the Northern Irish party, added that his party would not support the current deal set to be voted on in Parliament on Tuesday night.

Wilson, whose party props up May's minority government in Westminster with, told CNBC's Steve Sedgwick that a "no-deal" Brexit would spur the EU into fresh talks.

"I believe once we are in that situation, reality will kick in Brussels and they will come back and negotiate a realistic trade deal, rather than the one we have got at the moment," he said.

Wilson said lawmakers in Brussels would urgently seek talks in order to protect their large surplus on trade.

According to a U.K. Parliament report, the EU had an overall trade surplus of £67 billion ($86 billion) with the U.K. in 2017. A deficit of £28 billion on trade in services was outweighed by a surplus of £95 billion on trade in goods.

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