I am feeling more optimistic than I have for some time that there will be an agreement with the EU on Brexit. The prime minister and a large majority of her cabinet are well aware of the serious and lasting damage that would be done to British industry – at a cost of tens of thousands of jobs – if we exited the European Union next March without agreement and without any transition period.

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My improved humour is, in part, because of Theresa May’s success in getting the backing of the cabinet for a pragmatic British strategy at the Chequers summit.

It is true that we will have to live with, at least for some years, serious limitations to deregulating some of the laws affecting industry, and negotiating new trade agreements with third countries. But these constraints need not be for ever. As the dust settles, and as British industry adapts to us not being in the EU, we will be able to assert greater freedom even if, over the longer term, we sacrifice some automatic access to European markets. It might take five or 10 years but what is that in the life of a nation?

I am, perhaps, more relaxed than I should be over Boris Johnson’s and David Davis’s departures. The resignations of the foreign and Brexit secretaries are causing a short-term crisis, but a large majority of Conservative MPs do not support them. They are what the Chinese would call “paper tigers”.

Davis’s resignation is more principled. He offered it at a time when his Brexit colleagues appeared to have reached a separate decision. As the person required to take forward the negotiation it is understandable that he decided to call it a day.

Johnson’s behaviour has been disgraceful. Having insulted the prime minister at Chequers he then found, over dinner that evening, unconvincing reasons for continuing in her cabinet. Now he lamely follows in Davis’s wake.

On this occasion he might think that Michael Gove has again stabbed him in the back by supporting the prime minister and not his fellow Brexiteers after the Chequers summit. However, he should remember Churchill’s wise advice that politicians should not commit suicide because they might live to regret it.

In the longer term the most important development today will turn out to be not Johnson or Davis’s departure but Dominic Raab’s arrival.

The cabinet has not been purged of Brexiteers, and rightly so. Raab was a powerful and convinced advocate of departing from the EU during the referendum debate. But he has major advantages over Davis as he becomes our chief negotiator.

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Davis was good when he took the trouble to be, but there were long periods when he didn’t deign to take the trouble. Raab has a passion for work, intelligence and an attention to detail. The EU negotiator Michel Barnier will be dealing with a fellow professional rather than a relative lightweight.

The other major benefit is that Raab will be happy to work closely with May and her chief adviser, Olly Robbins. There will be a single British team, something that has not existed for some months.

But there is one further point that needs to be made. If Raab succeeds in his mission, we will have a highly credible new potential successor to the prime minister. John Major came from behind to claim the crown from Margaret Thatcher; this may be the day we see history repeating itself.

• Malcolm Rifkind is a former foreign secretary and former Conservative MP