Obviously, I know that politics and football are different. One is a high-stakes endeavour that affects the lives of hundreds of millions of people, with an impact felt around the globe and down the generations – and the other is politics. I know too that there will be plenty of readers who will be like I was until nearly a couple of decades ago: cheerfully indifferent to the beautiful game, even after a week like this one, when the top prize in English football was won. But stick with me, because there are lessons to be learned from what just happened – lessons for politics, for the prime minister and for all of us.

I am referring, of course, to Arsenal winning the Premier League, ending a 22-year long wait that it sometimes seemed would never end. I claim no objectivity here. I became a fan just a few years into that drought, brought into the Arsenal fraternity by my young sons. So there I was, in the crowd that instantly converged on the Emirates Stadium late on Tuesday night, Arsenal shirt and scarf on, singing loudly and beaming at strangers.

Keep politics out of sport, they used to say. But there are things politics could learn from sport – and specifically, from Arsenal’s long-awaited success. And before you dismiss as fanciful the very idea of politicians taking advice from the dugout, recall that it does happen: former Manchester United boss Alex Ferguson confirmed that Tony Blair once sought his guidance on how to manage a star player who refused to obey instructions. (The source of Blair’s trouble was the man in the No 11 shirt, Gordon Brown.)

Start with stability. Mikel Arteta took over in December 2019, a week after Boris Johnson won a landslide election. While Arteta has remained in his post, there have been four prime ministers, with a fifth presumed to be on the way. Downing Street has become like Chelsea, changing bosses with every bad run of form. But the Arsenal way is different.

Even when the team struggled – coming eighth in two successive seasons, which for a club of Arsenal’s standing is the equivalent of taking back-to-back wallopings in local elections – Arteta stayed put. In December 2020, Arsenal were in 15th place. At a moment when most clubs would have shown the manager the door, Arsenal stuck with their leader.

Call it strategic patience. The club owners had picked Arteta for the job and they gave him the time to do it. Strange to think that while politics demands instant gratification, it’s sport that can demonstrate the value of waiting.

Patience was the necessary companion to what has been a defining aspect of the Arsenal project: long-term thinking. I learned this week that the club has a “football intelligence unit”, which five or six years ago laid out a timeline and potential route back to the top. According to James McNicholas, who covers the club for the Athletic and is known to fans as Gunnerblog, the unit surveyed the competitive landscape, working out when Arsenal’s rivals might weaken, factoring in everything from the contract expiry of Manchester City’s Kevin De Bruyne to the expected physical decline of Liverpool’s Mohamed Salah. With that, they “plotted a potential window for Arsenal to come to the fore”, working out that the most propitious period would be the one we are in right now. “Everything strategically the club did was about fine-tuning, calibrating a squad to peak in that window,” says McNicholas. That quiet work went on in the shadows for years – and this week we saw the result.

Now compare that kind of long-termism, devising a plan and executing it, with the way government operates. It’s usually, and understandably, focused on the short-term – scrapping a planned rise in fuel duty, for example, to address immediate pressure on the cost of living, rather than advancing the gradual, necessary shift away from fossil fuels. The furthest horizon ministers can see is the next election; sometimes they can’t look beyond that day’s news cycle. On those rare occasions when government does attempt a truly long-term project, the results are too often disastrous: this week we learned of yet another over-run on HS2, set to cost more, take longer and deliver less than anyone ever agreed to.

Of course, patience and long-termism require a third element: a plan. Or, more grandly, a vision. And it’s this that makes Arteta’s achievement an object lesson for one of Arsenal’s best-known fans: Keir Starmer. “Arteta had a rock-solid vision in his 20s,” recalls my colleague Nick Ames, who got to know the Spaniard in his days as a player. Even then, Arteta had developed a philosophy of how the game should be played.

The same cannot be said of Starmer. His inability to articulate a vision for the country, or even a plan for this parliament, has been perhaps his greatest weakness. The PM’s defenders might say that he would have done fine, if only the voters had allowed him the space and time Arsenal’s owners granted Arteta. But that kind of patience has to be earned. And the way to earn it is by telling a story so compelling, people are prepared to give you the time to get to the end. Arteta did that, but Starmer never did.

An essential ingredient is hope. Arteta never stopped assuring fans that success was coming, that they could and should dream of the biggest prizes. But, from the start, Starmer lowered expectations, warning weeks into his tenure that things would only get worse. He confused optimism with complacency, moving quickly to stamp it out. People will walk through a storm with you if they think you’re leading them to sunshine. But if the destination is grim, or never adequately described, they’ll soon drift away.

Naturally, vision alone is not enough. It has to be combined with a pragmatic willingness to adapt when necessary – and by something else too. “Arteta is a control freak,” says Ames, noting that the Arsenal boss is across every detail, getting involved with what and when his players eat, adjusting the layout of the training ground, recruiting players personally. He has what politicians like to call “grip”. Contrast that with Starmer, who was happy to leave the handling of Peter Mandelson’s appointment as UK ambassador to Washington to others, with calamitous consequences. A PM who had read the Arteta playbook would have insisted on knowing everything, so he could make the right call.

Still, there are lessons from Arsenal’s victory that go beyond the fan in Downing Street and indeed Westminster. It’s worth saying, after this week’s tumbling migration figures were greeted with such delight, that Arsenal and the rest of the Premier League are only as good as they are because of migration, that ability to draw on talent from all over the world. But there is something deeper to say too.

It’s become commonplace to insist that Britain is broken, that multiculturalism has failed and that London in particular has become a shabby, fearful and unhappy shadow of itself. But that is not what I and thousands of others saw on Tuesday night. The impromptu crowd that assembled, the honking cars and the hugging fans, was made up of all those diverse communities, and generations, so often said to be at each other’s throats. And as longtime Gooner Piers Morgan noted, it looked a whole lot bigger than the rally summoned last weekend by Tommy Robinson, supposedly to “unite the kingdom”. The red kingdom of north London was united this week, in joy and pleasure and relief. Even if you can’t cheer the team – and if you’re not an Arsenal fan, why would you? – you can certainly cheer that.

• Jonathan Freedland is a Guardian columnist