Nick Hargrave is a former Downing Street special adviser, where he worked under both David Cameron and Theresa May. He now works at Portland, the communications consultancy.

Now that the Prime Minister has announced a timetable for her departure, the immediate question for the leadership contest that’s about to get underway is how to fix the Brexit paralysis.

Several candidates will be wrestling with whether Conservatives must now countenance leaving the European Union without a deal in order to sort the stasis and stop the rapid migration of votes to the Brexit Party. This is a question that is likely to intensify over the next few days as the European election results become clear.

My personal reaction is that this would be a very bad idea. It’s not my politics and – as a paid-up Tory member – I would have trouble voting for a party that prosecuted such an argument.

But I am aware I may be in a minority amongst the grassroots. So perhaps a more salient and objective question is whether the Conservative Party could win a general election this year with No Deal as its proposition. Many in the party are now No Deal advocates and – given the parliamentary numbers – it’s hard to see how a new Prime Minister could oversee that outcome without getting a fresh mandate from the country.

Opinion polling has uncertain currency given recent debacles. Nonetheless, recent studies on preferred Brexit outcomes – coupled with the current realignment on voting intention – offer some basis for a hypothesis. It’s not unreasonable to posit that at least 35 to 40 per cent of the electorate (maybe more) want us to get out of the European Union immediately. If that means walking away without a deal then so be it. With Labour’s position on Brexit clear as mud and the Liberal Democrats eating into their Remain voters, there is a clear surface case that the Conservatives could win a ‘no deal’ general election with a simple platform.

However, I am not sure this translates into a realistic analysis in a first-past-the-post electoral system.

First, there are the seats that the Conservatives would be putting at risk with a ‘no deal’ electoral strategy. In and around the capital you could see losses in such places as Wimbledon, Putney, Chipping Barnet, Hendon and Chelsea & Fulham. Beyond that, I wouldn’t fancy our chances in places like Pudsey, Milton Keynes South, Watford and Reading West.

The greater trouble though comes when you look at some of the seats the Conservatives would need to win to compensate and push on.

Ashfield. Bishop Auckland. Wakefield. Great Grimsby. Stoke on Trent North. Scunthorpe. Not a scientific sample but Labour constituencies with low majorities and Leave votes of more than 60 per cent in 2016. If the Tories cannot take these constituencies, then it’s difficult to see things going well given potential vulnerabilities elsewhere.

These were constituencies the Conservatives targeted heavily in the 2017 general election, but which didn’t shift. This was not just because Theresa May was a sub-par campaigner.

It was because gut nervousness about the Conservative Party ran deep in these seats, driven by the legacy of deindustrialisation in the 1980s. We haven’t thought about this enough in the past couple of years.

The slogan of ‘strong and stable’ is much remembered. Less well remembered is the mantra of the time that Theresa May was ‘a different type of Conservative’. This was calibrated to persuade target voters in these seats to discount their concerns and put their cross in the party’s box because of a shared commitment to implementing Brexit. It wasn’t very successful for a number of reasons – but not least because of the social care mis-step. Labour were able to seize on the policy and paint a caricature that the same old nasty Tories were lurking beneath the surface.

A prospectus for No Deal in the de-industrialised midlands and north could present a similar situation magnified.

Remove the bulldog platitudes from one side – and the doomsday predictions of the other – and consider instead the practical case for making the best of leaving the European Union without a deal. What would you actually be saying to the electorate?

Strip everything away and your case as a Tory is basically one of competitive edge. The alternative is some form of Bennite siege economy, but I think you’d struggle to carry the grassroots. So you’ll basically end up saying that we’ll beat the Europeans and their Single Market by pulling every lever we have to attract investment to our shores. You’d slash corporation tax. You’d water down corporate governance requirements. You’d prioritise the areas where the country is already strong like finance and professional services with rocket boosters.

It sounds simple written down like that and I’m sure it would go down well with some. But I am not sure it is a passport to success in the target constituencies I have outlined. Any half-decent campaign from Labour and the Liberal Democrats will argue that this is a charter for lower public spending and redundancies at the local manufacturing plant while the Tories look out once again for their mates in the city. Singapore on Sea or equivalent. Some of this will be overheated. So was the dementia tax. That’s the tough reality of politics.

So putting No Deal to the electorate risks losing Conservative votes in some areas and failing to win new ones in others. And that’s before you get into whether to deselect incumbent MPs who don’t sign up to the platform.

What then are your realistic political alternatives if you’re running to be Conservative Leader and want to stay in Downing Street for more than a few months?

You could try and say that your powers of persuasion are better than Theresa May’s and you can sell the existing Withdrawal Agreement to this Parliament. It feels like things have come too far for this to be realistic.

You could say that all we need is to knock some heads together and fix the technology on the Irish border so we don’t need a backstop in the Withdrawal Agreement. But if you really believe that the issue here is to do with technology rather than a century of psychology then you are likely to be disappointed.

You could throw the DUP to the wolves and fix the backstop by agreeing that it should only apply to Northern Ireland if it’s ever needed. Irrespective of whether you could get anything done without your confidence and supply partner, there would be serious implications for stability in the province.

You could call an election and do a non-aggression pact with the Brexit Party where they focus on the legacy Labour strongholds. It’s not inconceivable but you’d better be prepared for Nigel Farage to have more seats at the end of the night than you.

Or you could just be honest. After the political paralysis of the last few months, Brexit – negotiated or otherwise – is not going to happen without some form of new mandate from the British people. So if you’re feeling queasy about changing the Parliament…perhaps it’s time to begin thinking about changing your policy on a second referendum. What’s the point otherwise?