Gareth Southgate will stand once more on the sidelines on Sunday evening in Veltins arena in Gelsenkirchen, wearing his cream polo shirt and familiar ruminative expression, and watch his team attempt to beat Slovakia to advance to the quarter-finals of Euro 24. But whatever unfolds during the match, it seems increasingly likely that this tournament will be his last in charge of the England men’s football team.

He’s always maintained that he doesn’t want to outstay his welcome and would avoid being “in a position where my presence is affecting the team in a negative way”.

That position, alas, is not dissimilar to where Southgate now finds himself. England arrived in Germany as favourites with a team featuring the Bundesliga’s top scorer (Harry Kane), La Liga’s player of the year (Jude Bellingham) and the English Premier League’s player of the year (Phil Foden). But they have under­performed, looking by turns sluggish and frenzied, but nearly always disjointed.

Like many, or arguably all, England managers before him, Southgate has become the object of intense criticism, not just from fans and journalists but also the England stars who are now TV presenters or pundits.

When Gary Lineker described the England manager as “tactically inept” and the team’s performance as “shit” after the Denmark game, it marked a new level of disaffection that was reinforced by fans throwing plastic beer cups at Southgate after the goalless draw against Slovenia.

The journey from hero to zero can be disorientingly rapid in international football management, where Newton’s third law of motion has been rewritten to become: every action has an unequal and hysterical overreaction.

Lineker himself acknowledged the dramatic reversal. “It’s really hard to be critical of Gareth Southgate,” he said, “because, overall, he’s turned England’s fortunes around in many ways.”

Yet the 53-year-old has cut a slightly dispirited figure in this tournament, as if baffled not just by what his best team might be but also at the strength of vitriol that has come his way.

It’s only three years since he guided England to the final of the delayed Euro 20, on the eve of which he wrote a celebrated letter to the nation. Addressing his readers as “Dear England”, he paid testament to the difficulties of Covid and the lockdowns, and praised the character and patriotism of his players, who he said represented a movement towards “a more tolerant and understanding society”. He also informed racists that he had some bad news for them: “You’re on the losing side.”

The letter inspired the playwright James Graham to write Dear England, which became a West End hit, with Joseph Fiennes brilliantly capturing Southgate’s inquiring approach to questions of masculinity and sporting success.

In the play Southgate is portrayed as fundamentally decent and caring, which is very much the character described by those who know him. The veteran ITV commentator Clive Tyldesley, who considers Southgate a friend, has observed 11 different England managers at close quarters.

“I will leave judgements to others, and plenty are already weighing in,” he says, “but of all the people that I’ve known who’ve occupied this job, I don’t think I’ve ever come across a better person to deal with the widespread responsibilities.”

Tyldesley singles out Southgate’s intelligence, reason and balance as notable qualities, and warns that his detractors should “be careful what they wish for”.

“It’s almost as if we get bored with someone who’s good at conducting himself and delivering an England team which, to a large degree, realises its potential. Suddenly we want the guy that jumps up and down on the touchline, or the foreign guy, or anyone who’s the complete opposite of what we’ve already got.”

Southgate has said that he is “oblivious” to Lineker’s comments, but Tyldesley thinks it’s impossible not to be hurt by the criticism, especially from former professionals. “You can’t hide away from it in the 21st century,” he says. Recently the commentator talked to Southgate about watching one of the election debates between Rishi Sunak and Keir Starmer in which the final question was on Southgate’s style of management. “He laughed about it,” says Tyldesley, “but there’s literally no escape.”

Except, perhaps, through a rousing victory. That wouldn’t remove the spotlight from Southgate, but it might feel less like an interrogation lamp.

Despite his largely positive eight years as manager – the longest stint since Bobby Robson in the 1980s – Southgate is no stranger to adversity in the international game. As a player he missed the crucial penalty in the shootout against Germany in the semi-final of Euro 96.

That was back in the hog-mad days of the tabloids, and Southgate was besieged by doorstepping hacks. He said he felt like crawling away into anonymity, but he later reflected on the experience with typical stoicism.

“It’s hard not to lose touch with reality when you’re on the front three pages of every paper,” he said. “But there are far worse things that can happen. And the next day you still have to pay the telephone bill and the gas bill.”

He will doubtless bring a similar perspective to his current woes.

Graham has previously suggested he might change the end of Dear England, which is due to return to ­theatres next year, if England win this tournament. That may seem unlikely at the moment, but stranger things have happened, particularly in football. It would certainly make for a more satisfying conclusion to the play, but more importantly, it would be a fitting reward for a thoroughly good man’s efforts.