Dominic Grieve does not immediately strike you as a man prone to controversy. On a Wednesday afternoon interview in his Westminster office, he begins by reflecting on his time in parliament: “I had 13 years in opposition, which were difficult, and a very interesting just over four years in government, which I’m sorry came to an end.”

This understated appearance is misleading. In June, the unofficial leader of Remain-supporting Tory MPs was causing havoc for the Government. Now, after a quiet summer of non-interference, he is again voicing his disquiet with the road to Brexit, to the extent that he is for the first time backing a second referendum as put forward by the People’s Vote campaign.

That is in part because of what he sees as the inadequacy of Theresa May’s Chequers proposal. It “downplays the potential consequences of our leaving with no services arrangement,” he says. “The consequences are going to be very marked, thousands of jobs will leave London and go elsewhere.”

Grieve is also direct in his criticism of the Prime Minister, in particular her refusal to lay out whether she thinks Britain will benefit from Brexit: “she has had a policy of closing down the consideration of alternative options.”

“It is noteworthy that every time she is asked the question ‘do you believe the United Kingdom will be better off when we’re gone?’ She refuses to answer, or she diverts to a different answer.”

If a Chequers-style agreement is presented to parliament, however, he is unsure if he would vote against it: “as a parliamentarian I want to consult and listen to the views of colleagues.”

“I’ll listen, principally, to those of my colleagues who share my immense disquiet about what Brexit is in practice going to do to our country, and lurking behind that is undoubtedly the question as to whether we should go back and consult the public.”

It sounds like obfuscation. “If I could see a way through to ensuring that the public has an opportunity to consider afresh the options, that would be, undoubtedly, an influencing factor on my decisions”, he explains.

“After all, politics is the art of the possible. It’s very nice to be a rebel saying, ‘I stand on my principles’, but if in fact that’s not going to have any impact on the policy, it may be principled, but it doesn’t deliver the better outcome that the country needs.”

Grieve hasn’t previously endorsed the People’s Vote campaign, though this month he was listed as a member of their Advisory Committee in a report entitled The Roadmap to a People’s Vote. “I am supportive of their aims, there is absolutely no doubt about that,” he tells me.

When pushed to expand, he remarks: “I certainly think that a second referendum would be a desirable outcome, because I think that it will produce the clarity which otherwise is going to be wholly lacking.”

“It’s difficult to see what’s better. The only option is if, in some extraordinary way, the Prime Minister and the Government were able to put together a package that so commanded broad consensus in Parliament as being the best way forward,” he says. “I think that is incredibly unlikely, and if that doesn’t happen, my preference would certainly be to have a People’s Vote.”

While Grieve acknowledges a second vote could take many possible forms, what’s important, he argues, is that “people shouldn’t feel they are being cheated.”

“The only point of having this referendum is to have an honest consultation.”

He describes three ways it could be legislated for. His first (and preferred) approach is to persuade the Government to advocate the policy, where they “would have very little difficulty getting a majority.” If the government refuse, supportive MPs could “produce a majority in Parliament which the government is then prepared to go along with.”

His third suggestion is more drastic. “Alternatively, somebody has to set up a government to deliver it”. Although admitting the plan is “highly speculative”, Grieve continues candidly: “but it would only be to deliver it because the reality is that no such government would then be able to continue.”

“It would be fairly radical. Ultimately, any government is one which enjoys the majority of support of members of Parliament to carry out a policy. So, it would have to be on a cross-party basis.”

Under the 2011 Fixed-term Parliaments Act, this would require a motion of no confidence in the government, and in practice, the votes of around a third of Conservative MPs. Grieve indicates this might not be as unlikely as it seems: “Albeit MPs won’t admit it publicly, but if you go around and speak privately to people, there is a very curious level of majority consensus in my view that the Brexit process is very risky, that no deal is an unacceptable outcome, and that any deal brought back by the government, however worthy it may be and however well negotiated, is likely to have serious downsides to it.”

I conclude by asking if the Conservatives will ever recover from their divisions over Europe. “I think it’s very difficult to say”, he says frankly. Grieve understands the possible consequences a second referendum would have for his party. “If we remained for some reason, it would be a matter for those such as Jacob [Rees-Mogg] as to where they wanted to be.” He clarifies: “It would be a matter for them whether they wanted to stay in it or not.”

It all sounds like a mess. “I’m longing for it to be over”.