In a heated Brexit debate, Mr Grieve claimed Brexit is a “very bad idea” before admitting he is “almost certain” Britain will eventually leave the EU.
Speaking on BBC Radio 4’s Today programme, Mr Robinson said: “There may be people who say ‘well why should we trust you, Mr Grieve?’ You are opposed to Brexit.
“You had a meeting the other day with people whose life’s work is to reverse this referendum with people like Alastair Campbell and others.
“The truth is, you don’t believe in the will of the people, isn’t it?”
In response, Mr Grieve said: “That’s not the case. I think one has to face up to the fact that it’s possible for me to think that Brexit is a very bad idea, which I do.
“That’s why I campaigned for Remain and my own opinion hasn’t changed. It’s also possible for me as a parliamentarian to try to make sensible steps to manage what I see as an inherently risky process, which in all probability I think is going to lead to us leaving the EU.
“That’s what is almost certain to happen. I also have to pay attention to that.”
Mr Robinson also quizzed the Tory Remainer about a recent meeting he had with the “leader of the Brexiteers” Jacob Rees-Mogg.
In response, Mr Grieve said he knows Mr Rees-Mogg well and insisted the pair must “cooperate together if we are going to get through the Brexit process”.
Last week the Prime Minister only just managed to persuade potential rebels to back down minutes before a crunch vote to an amendment scheduled by Mr Grieve – demanding measures be put in place to avoid the UK leaving with “no deal”.
But the Tory rebels later rejected the wording to the Government’s “meaningful vote” amendment and said it would give MPs no chance to prevent a “no deal” Brexit if there is no agreement with Brussels by January 21, 2019.
Rebel MP Anna Soubry said the last minute change to the wording of the amendment was “unforgivable” and “very disappointing”.
In response to the change, Mr Grieve said despite being aware of the possible catastrophic consequences of his actions, he would pursue a vote against the Government’s Brexit bill next week if concessions are not made before then.
The former Attorney General told BBC Sunday Politics: “We could collapse the government. And I assure you I wake up at 2am in a cold sweat thinking about the problems that we have put on our shoulders.
“The problem is that the Brexit process is inherently risky. Really risky.
“Risky to our economic well-being, to our international relationships and ultimately to our national security.”
The Tory MP denied sabotaging Brexit was his end goal despite a torrent of criticism from Brexiteers.
But when the Government’s “meaningful vote” amendment was sent back to the Lords on Monday, peers voted resoundingly by 354 to 235 for an amendment which will give MPs a greater say if the Government fails to achieve an acceptable Brexit deal by February 2019.
The amendment was tabled by Lord Hailsham after Mr Grieve demanded MPs should be given the power to vote on the final Brexit deal.