Former attorney general Dominic Grieve, whose amendment inflicted the Government’s first defeat in the EU Withdrawal Bill debate, will join Labour’s Chuka Umunna and Conservative MP Anna Soubry in Brussels to meet Mr Barnier as thoughts turn to phase two of Brexit talks.

Labour MPs Chris Leslie and Stephen Doughty, who are both keen for the UK to retain its single market membership, will also attend.

Mr Barnier is understood to be keen to hear the views of British MPs on Brexit as well as Government figures.

Speaking ahead of the meeting, Mr Grieve said he was looking forward to what he described as a “fact-finding mission”.

He said: "It will enable me to have a better understanding of the EU's position on Britain's withdrawal."

Mr Grieve also dismissed claims by Labour's shadow foreign secretary Emily Thornberry that the Government may try to overturn the amendment which forces a Commons Brexit vote when the EU (Withdrawal) Bill returns to Parliament this week.

He said: "There is no sign of the Government attempting to do that."

The meeting comes as pressure grows on Labour leader Jeremy Corbyn to support continued membership of the single market and the customs union.

The Labour leader has insisted the UK cannot remain a member of the single market unless it remains in the EU, which several of his own MPs dispute.

Norway, Iceland and Liechtenstein all participate in the single market and Mr Umunna believes Britain should aim for a similar relationship with the EU.

He told Sky News: “There’s no reason why the UK, if we leave, should not have that kind of relationship.”

Despite the Government repeatedly ruling out the prospect of keeping Britain’s customs union and single market membership after Brexit, the SNP is keen to bring the idea back to the negotiating table and are looking to other opposition parties to support them.

The SNP, Liberal Democrats, Plaid Cymru and the Greens are set to back a separate amendment this week that would prevent ministers being able to take the UK out of the single market and customs union without the approval of parliament, but Labour MPs are not expected to back it.

The meeting in Brussels will be the second time in just a few days that the EU’s chief negotiator has met with UK diplomats to discuss Brexit.

Last week, Mr Barnier met with representatives of the Leave campaign including former Ukip MEP Steven Woolfe, Lord Digby Jones, the former director of the CBI, Labour Leave’s John Mills and Leave Means Leave’s John Longworth.

The delegation travelled to Brussels to defend the position of Leave voters before talks resume in Brussels.

And the group presented Mr Barnier a hamper of cheddar cheese, English sparkling wine and Shakespeare plays in an attempt to convince him not to underestimate the UK’s position on the world stage.

Speaking after the meeting, Mr Woolfe said: “We told him that a trade deal should include goods and services.

“Our message was that if we don't have an inclusive agreement for goods and services, the British public will say we should walk away with no deal.”