This week, the One Nation Caucus of Conservative MPs has invited all leadership candidates to our hustings. They are the first official gathering of this lively leadership contest. Nicky Morgan, Sir Nicholas Soames, Damian Green and I recently re-formed this now 60-strong group of MPs, and we are keen to understand how the candidates in the race intend to break the impasse with the EU so we can leave with a deal.

The debates will begin on Tuesday and be chaired by Katy Balls and Matt Forde.Beyond Brexit we want to hear the ideas that candidates have for improving household finances, for education, for welfare and how they’ll use Britain’s standing in the world. But to get to that point we have to solve the Brexit puzzle.

Amber Rudd warns Tory leadership candidates against backing no-deal Brexit Read more

That means practical proposals to navigate the reality we face. It should go without saying that every candidate is patriotic. Being told to just “believe in Britain” is not a substitute for engaging with the situation we find ourselves in.

There are a few inescapable facts that cannot be wished away:

• The new prime minister will inherit the same parliamentary arithmetic as the current prime minister. That means a tiny majority – and only if the DUP, the ERG and the steadfast Remainers can all be convinced to back the same deal.

• Under the terms of our current extension, it is not possible to renegotiate the Withdrawal Agreement before 31 October. That was agreed by the UK in the April European council meeting. And the new European commission will not be fully in place until 1 November.

• A majority of MPs oppose leaving without a deal. With the current Speaker, it is likely parliament will find a way to once again insist we do not leave without a deal, regardless of what recent reports suggest.

So we need to start being honest. We are not leaving on 31 October with a deal – parliament will block a no-deal Brexit, and there isn’t time to do a revised deal.

So what happens next? A general election would risk bringing in a Labour leader whose damaging policies make Ed Miliband look moderate. A referendum would be parliament admitting it has completely failed to come up with a solution.

So let’s be straight with the British people.

Whoever becomes the new prime minister will have done so after winning the support of MPs and 160,000 members. They will immediately have the opportunity to chart a new, positive vision for Britain. They can use that to enter into another battle with parliament over no deal on 31 October, which is something the public find infuriating. Or they can find a new way – a course of action that would keep the British economy strong, and also give the new prime minister the chance to offer Britain a better future that grasps the opportunities Brexit can offer. But there’s a catch. If the Conservatives and the DUP can’t rally behind a compromise, then a deal would have to be done with some Opposition support.

Understandably, the EU will only engage if they see a genuine opportunity to make progress. They’ve already seen the previous deal fail three times.

So to make any progress we need my backbench colleagues on the government side to engage – otherwise the only way through is working, again, across the House. There is no other way to find a majority.

To make any progress we need my backbench colleagues to engage across the House Amber Rudd

Many good Conservative colleagues will raise their hands in despair at my suggestion that we engage with Labour backbenchers, but I know there are many who wish to deliver on the result of the referendum.

I certainly hope my idea is not the only one. After the recent European elections I understand the temptation to deliver Brexit at any cost, but the best option for our country is a renegotiation.

There are few good choices available here. But it is my view that a new prime minister should seize the opportunity to sit down with the new EU commissioner on 1 November and negotiate a new deal for Britain.

At the hustings this week I want, and hope, to hear more ideas, with the majority of candidates saying they want a deal with the EU. So it is my view they should be realistic about the practicalities of negotiating one.

Even some of the “hardest” Brexiteers say they don’t, ideally, want to leave without a deal on 31 October. So let’s make it possible by having a new deal. Many will point out that that’s not what’s been offered by the EU. But our circumstances will have changed when we have a new PM.

The new prime minister has a brief opportunity to reset the political agenda. This moment is too important to rush.

It’s time we thought about what we want Britain to be in 90 years, not 90 days. I hope all candidates grasp this opportunity and I look forward to welcoming as many of them as possible this week.

Amber Rudd is the secretary of state for work and pensions and is co-leader of the One Nation Caucus of Conservative MPs