Such a move would signal a direct reversal of the path outlined by May, but the 20 MEPs say that failure to do so “would leave Britain poorer.”
The group includes three Tories and 12 Labour MEPs.
In a letter, the group say that the case for staying in the internal market has become stronger since the 2016 referendum.
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It reads, “The best way to secure Britain’s prosperity would be to remain close to Europe, inside the single market and customs union, and to secure a deal that keeps Britain in the room.
“Sadly, this no longer seems likely. So, if the price of a Brexit turns out to be a loss of control over the rules and an economy that will leave us poorer, people have every right to keep an open mind about whether the Brexit course chartered by our government is the right path for our country.”
They call it a “lamentable irony” that Britain helped shape the single market but that successive governments have failed to make the argument for its benefits.
“Leaving the EU means giving up our seat at Europe’s top table and risks making us a rule taker rather than a rule maker.”
The signatures include UK Tory Charles Tannock, who described the 52 per cent victory for Leave in the EU referendum as a margin “not convincing for Brexit, let alone the hardest of Brexits” given the scale of constitutional change. He argued that other countries would demand a super majority for something so critical.
His two colleagues, Julie Girling and Richard Ashworth, who have also signed the letter, remain members of the Conservative party but have had the whip withdrawn over a recent vote in the European Parliament.
Meanwhile, a delegation of pro-Brexit politicians will meet this week with the EU’s chief Brexit negotiator, Michel Barnier, in order to demonstrate that there is “huge support” for favouring trade on WTO rules over a bad Brexit deal.
The organiser of the meeting, independent MEP Steven Woolfe, said Barnier’s recent meetings with largely anti-Brexit British politicians has resulted in “a bit of an echo chamber”, and added, “We want to show a bit of strength, that there is an iron will behind the negotiations to give support to our politicians and our civil servants
Elsewhere, speaking at the weekend, May said that a Brexit deal would be reached this year, adding, “I’ve been very clear that, by the time we leave the European Union, we want to have agreed what the future relationship between us and the European Union is going to be. Michel Barnier himself has said he wants that agreed by October of this year.”
She told the BBC, “It would be a free trade agreement which we want to cover both goods and services and what I want to do is to ensure that as we look at the Brexit deal going forward it’s important we recognise why people voted to leave the European Union here in the UK.”