We will have a new prime minister but the task facing them is the same one Theresa May faced for three years: how do we deliver the 2016 referendum result in a way that is good for the prosperity, security and integrity of the UK?

If anyone thinks this is an easy task, they don’t understand the magnitude of the situation. Having served in her cabinet, I know that no one could have worked harder or shown greater determination than Theresa May to find a way through.

Brexit will dominate this leadership election. But too often, the debate on Brexit has failed to face facts. It has been characterised more by wishful thinking than a clear-sighted appreciation of the economic, diplomatic, parliamentary and political realities. Big promises fail to be delivered, leaving the public yet more disillusioned, angry and tempted by the snake oil of populism.

Stop Boris campaign launched by Tory moderates opposed to no-deal Brexit Read more

Speaking as one of the few Conservative MPs who do not aspire to be elected leader in July, all those who have such aspirations have a responsibility to set out an approach to Brexit anchored in the hard realities of the situation.

First, we should not pretend that leaving the EU without a deal will be anything other than enormously harmful to our economy, weaken our security relationships and threaten the integrity of the union.

Businesses that rely on access to European markets – whether for exports or supply chain imports – will become unviable. Good jobs will be lost, investment diverted, the public finances weakened and living standards damaged by higher inflation caused by a weaker pound.

There is too often reluctance in pointing out the likely outcome of no deal. The pretence that no deal is somehow manageable by people who should know better has encouraged a growing part of the population to be unwilling to make any kind of accommodation with the EU. Loose talk about no deal has given credibility to the simplistic slogans of the Brexit party and resulted in millions voting for them.

If a candidate believes in a no deal exit, they should be straight with the British people that it will come at a very considerable cost. That cost won’t be wished away by glib assertions that we should simply have “confidence in Britain” or about how we overcame adversity in the second world war.

The Tory party is simply debating which sort of electorial cyanide to take Read more

The second hard reality is that there is no easy alternative option waiting to be negotiated with the EU. The withdrawal agreement is highly unlikely to be re-opened but changes in the political declaration might be possible. Even so, the EU is not going to agree with an arrangement that allows us to abandon our commitments under the Good Friday Agreement. If Northern Ireland is in one customs regime and the Republic of Ireland is in another, why won’t a customs border be necessary, just as happens with every other land border of this type? Technology may well be the answer, but it is not ready yet. Let’s not kid ourselves that this is not a genuine problem.

This is why we should be particularly sceptical about claims that the EU offered us a free trade agreement. It was an offer not to the UK but to Britain only, and for a very good reason – because if you include Northern Ireland in a Canada-style free trade agreement, you have an issue with the Irish border. But an offer which only works for Britain is not a solution that should be acceptable to the Conservative and Unionist party.

The third hard reality is about the parliamentary numbers. To leave the EU with a deal, we need a parliamentary majority. Theresa May tried and failed three times. Too many Conservative MPs have been unwilling to support the necessary compromises. I hope a new leader may win more of them over. But the likelihood is that we will need the support of some Labour MPs. This will need cross-party co-operation and compromise. Parliament will be able to shape the contents of any withdrawal agreement bill and, as a consequence, a Brexit deal delivered in this parliament will not be as purist as some of my colleagues want.

That may lead some to argue that we must have a general election to deliver a Conservative Brexit. You don’t have to have a long memory to realise the risks with this.

The fourth hard reality is that a general election before the issue of Brexit is resolved is more than likely to put Jeremy Corbyn in No 10.

So who should be our next prime minister? I have not yet decided who I will support. But only a candidate who rejects wishful thinking, has the courage to tell the truth about the options in front of us and who will address Brexit on the basis of the hard realities will succeed.

• David Gauke is lord chancellor and secretary of state for justice