The political heavyweights clashed on social media over the Irish border, which has proved to be a log-jam in Brexit negotiations.
It came after EU Council President, Donald Tusk, confirmed on Twitter the EU was going to offer the UK a Canada style Brexit deal.
Mr Rees-Mogg, head of the European Research Group (ERG), replied: “This is a good solution for everyone and the ERG’s proposals for the Irish border mean it could work for the UK as a whole.”
But David Lammy, arch-Remainer and Labour MP for Tottenham, retorted with a furious tirade against the Somerset MP.
Mr Lammy said: “We’ve had quite enough of your proposals for the Irish border.
“You’re on tape calling for people to be ‘inspected’ as they were ‘during the Troubles’.
“This disdain for the Good Friday agreement is shameful and no solution at all.”
Lots of social media users agreed with the Remainer’s reply.
One said: “Nobody will be ‘inspecting’ me in my own country.”
Another added: “You are so right David to imperil peace as if it were a trifle totally unacceptable.”
And another accused the Brexiteer of wanting to return to the troubles, saying: “Mogg misses the war.”
But others leapt to Mr Rees-Mogg’s defence.
A woman from Derry replied to Mr Lammy saying: “Here’s a novel idea: how about asking the peeps ACTUALLY LIVING in NI for their opinion?”
Another social media user, from England, said: “Lammy is a troublemaker and rabble rouser. He doesn’t want solutions or constructive dialogue.
“We agree with the EU President and will work with him.”
And another added: “Wrong again David Lammy, the Moggster wipes the floor with you every time, any day of the week!”
The European Council President envisaged a future relationship with the UK as a “Canada plus plus plus” arrangement, which could be “much further reaching on trade, internal security and on foreign cooperation”.
He added: “This is a true measure of respect. And this offer remains in place. The EU is serious about getting the best possible deal.
“Even though we haven’t changed our minds that the consequences of Brexit will be negative, for both sides.”
The EU’s chief negotiator Michel Barnier has previously spoken of the possibility of such a deal being pursued, but critics in the UK believe it doesn’t fully address the Irish border.
Brussels is now hoping the end of the Conservative party conference will bring a fresh attitude to talks as both sides strive to complete a deal on the Irish border as early as the upcoming October summit and the rest of the withdrawal deal by November.