In Boris Johnson’s first public outing since securing a historic victory for the Conservatives, the prime minister laid bare the challenge that lies ahead for his party. Just after 7am, in a hall filled with bleary-eyed staffers and journalists, Johnson thanked the new Tory voters who had helped return his party with its best result since 1987 – before attempting to offer them reassurance: “I will make it my mission to work night and day, flat out to prove that you were right in voting for me this time, and to earn your support in the future.”

As it looks ahead to a fourth term in government, the Conservative party has been transformed. The Tories didn’t just make a dent in Labour’s so-called red wall – of traditional heartlands in Wales, the Midlands and the north – they practically demolished it. They unseated Labour politicians including Laura Pidcock, Melanie Onn and Dennis Skinner as they turned once unlikely seats such as North West Durham, Great Grimsby and Bolsover blue.

Play Video 7:41 'We smashed the roadblock': Boris Johnson's election victory speech in full – video

A realignment of British politics is under way. It has already changed the make-up of Johnson’s party: it is now formed of a coalition that ranges from remain metropolitan areas such as Kensington and Cities of London and Westminster to swathes of traditional Labour towns that voted to leave. Johnson is at pains to make sure that latter group feels at home permanently, and he used his appearance this morning to vow that he would rise to this task with a “people’s government”.

In theory, he has the space to do just that, with a majority of just under 80. In the buildup to polling day, there were nerves among ministers over how the Tories would govern if they mustered only a small majority. As one cabinet minister told me, it really had to be above 12 and ideally 15 if the party was going to be able to bring about significant change. The scope with this majority is vast.

Even if his charm offensive falters in the future and he fails to convince everyone of his choices, it won’t be fatal

Johnson is free to choose to govern as he wishes. He is not beholden to any particular Tory faction. The power of the European Research Group of Tory Brexiters has today been reduced significantly. Likewise, were any Tory MPs to get squeamish about the idea of a hard Brexit, they would likely be given short shrift.

Expect Johnson to use this newfound freedom to try to accommodate the Labour leave areas that have gone blue. There were early signs of this during the campaign, with a manifesto in which the Tories pivoted to higher spending and moved to the right on law and order. The spending plans weren’t to the taste of some low-tax Tories, but one member of that group tells me they have since come to terms with the idea this won’t be a government of mass tax cuts.

The biggest challenge, however, will be Brexit. Although Johnson has been keen to tell anyone who will listen that he has an “oven-ready” deal, this is just the first stage. Next, he must decide and negotiate the UK’s trade relationship with both the EU and the rest of the world.

This presents trade-offs. The former Labour leave voters who have turned to the Tories in this election share with Tory Brexiters a desire to get Brexit done. However, they won’t all be on the same page when it comes to trade.

Where there are some longtime Conservative MPs who view Brexit as a route to Singapore-on-Thames, former Labour voters are likely to be more protectionist. Johnson attempted to appeal to such a viewpoint during the campaign when he promised to shake up state aid rules for the UK after Brexit in order to make it easier for the government to help struggling British companies – proposals that caused dismay among several libertarian rightwing thinktanks.

Expect more of this in the coming months and years as the Tories adjust to their new coalition of voters. Johnson is reasonably relaxed on moving to the left on the economy where needed. He has even – retrospectively – voiced his discomfort with the austerity championed by some of his Tory colleagues.

As Johnson proved with his Brexit deal, which did the unthinkable and united what was left of the Tory party, the prime minister has the ability and confidence to sell his Brexit decisions in a way Theresa May never could.

But even if his charm offensive falters in the future and he fails to convince everyone of his choices, it won’t be fatal. He can now afford to put a few noses out of joint as he tries to forge a new centre ground. Besides, after delivering the best Tory result since Margaret Thatcher, even Johnson’s critics within the party are open to trying a new tune.

• Katy Balls is the Spectator’s deputy political editor