PRIME Minister Theresa May is in a jam – and not the sort that she eats after removing the mould – but intriguingly, could one of our three Brighton and Hove MPs have found her a route out?

Let’s begin with a reminder of how we, or she, got into this mess.

For the last year or so of the painful Brexit negotiations Mrs May has allowed herself to be bullied by Jacob Rees-Mogg’s so-called European Research Group – I say “so-called” because I have yet to see one single piece of research emanating from this set of recalcitrant MPs.

They have been going through the pretence that they are serious about helping Mrs May negotiate a withdrawal agreement but after every concession they demand more.

She was defeated on Thursday, her 11th defeat on European Union matters, because of the suggestion in the motion that MPs were against taking no deal off the table, which overwhelmingly they are.

Mrs May reportedly left Parliament fuming, as well she might, having been reassured earlier that the ERG was now “on board”.

Even if a deal is reached that breaks the deadlock over the back-stop (the arrangement that would govern trade between Northern Ireland and the Irish Republic during the post-deal transition period) the ERG would find another reason to vote against.

The majority of MPs have made it clear that they do want a deal, almost any deal, rather than tumbling over the no deal cliff.

Incidentally, those who think “no deal” is a negative term for trading on World Trade Organisation terms, need to think again.

The latest forecast of the impact of trading on WTO terms is a reduction in average income in the UK of eight per cent.

So what’s all this to do with the MPs from Brighton and Hove, all of whom are implacably opposed to the UK leaving the European Union?

To begin with one of the Remain camp’s leading lights; Caroline Lucas, the Green MP for the Brighton Pavilion constituency, not content with just preaching to the converted, has taken her campaign to some of the strongest Leave-voting areas of the country.

I am not suggesting as a direct result of her campaigning, and I share most people’s scepticism about the polls, so I mention without comment that the average lead for Remain, if there were a second referendum, is now around seven per cent.

Then there’s mace-waving Lloyd Russell-Moyle, the Labour MP for Brighton Kemptown.

He makes no secret of his admiration for Jeremy Corbyn but, notwithstanding, he has been one of the leading Labour campaigners telling the Labour leader that he must now put into practice the policy that was agreed at the last Labour conference – that if calls for a General Election fail then the party will campaign for a public vote.

Finally we come to Peter Kyle in Hove, on the opposite side of the Labour Party from his Kemptown colleague, but who shares with him an enthusiasm for the UK remaining in the European Union.

Mr Kyle has come up with the intriguing idea that MPs should support whatever deal Mrs May is able to cobble together – on condition that it is then put to a referendum with the ballot paper offering people the choice between her deal and remaining within the European Union.

It is unlikely that his amendment will win a majority in the House because of opposition by both front benches.

Indeed its chances of being selected for debate by the Speaker are not high.

But give it a moment’s reflection and it makes sense.

The overwhelming majority of MPs are against leaving without a deal, hence whatever Mrs May finally agrees with Brussels, with some support from Labour MPs representing Leave constituencies, will get through Parliament.

It will be closer to a “hard Brexit” than a soft one and will probably involve the UK leaving both the customs union and the single market, the two institutions at the heart of our membership, so for all but the extreme Leave risk, this delivers, in large measure, what they have been wanting.

But by putting the deal to a referendum it gives both the 52 per cent who voted to leave the European Union and the 48 per cent who voted to remain, a chance to have their say on what leaving actually means.

Some say that a second referendum would increase divisions in the country, but surely the chance for both sides to have a final say is as likely to heal as it is to divide?

After all what do we have to lose?

Ivor Gaber is Professor of Journalism at the University of Sussex and also a former political correspondent based at Westminster.