So: here we go again. England, unexpectedly, expects. There is something wearily familiar, but also irresistibly chipper, about the customary boomeranging of public sentiment when it comes to following England's footballers at a major tournament. For all the usual backdrop of scepticism, history shows most of the time all it takes is a single victory for hopes of improbable glory to begin to stir once again at the fringes like rabbits in the tree line.

Things were meant to be different this time. Euro 2012 was supposed to be the tournament of no ties, no strings, no expectations. Constructed on the hoof as a coat-hangered quick fix, Roy's Two Banks Of Four – often rejigged under pressure to one bank of 10 – travelled to Krakow, Donetsk and Kiev so unbowed by expectation that even this lack of momentum was hoist by some as a kind of passive‑aggressive secret weapon, seed perhaps for an ultimate triumph of English self‑deprecation.

True to form the mood ahead of the final group match against Ukraine in Donetsk on Tuesday has shifted a little following the rousing 3-2 defeat of Sweden in the Olympic Stadium, a victory made all the more satisfying by the rare spectacle of an England team responding to mid-game adversity with verve and resilience.

This time, though, a more unexpected transformation has taken place. Nobody has, as yet, suggested England are going to win it. Actually, that's not true: Alan Shearer has. But in a broader sense something else has happened: England have become likeable again. Not overwhelmingly so. But if the Guardian's new and entirely scientific online England happiness metre is anything to go by, they are at least reaching new peaks of understated public approval.

This is quite a feat for a team who in the dog days of the Fabio Capello interlude were as unpopular as England have ever been, cast in the public mind as a reluctant band of gilded underachievers. There have been some progressive adjustments at this tournament, a generalised atmosphere reboot around the squad. The relative openness, with the players free to go on – albeit heavily accompanied – walkabouts in Krakow has been refreshing. Plus there is a sense of slightly reined in extravagance all round with England for once some way off being the biggest spenders on personal arrangements: Portugal top the list, running at €34,000 (£27,000) a night, with England in the middle on a moderate-ish €19,000 a night.

If there has been a sense of affection-uplift among England's very loyal travelling support this is still not something to be taken for granted. Stan Stansfield is among those following the team in Ukraine. "I was in South Africa [at the World Cup]," he said during transit to Donetsk on Monday. "They interviewed me on TV after one of the games and I said, 'I don't really know what I'm doing here.' The team looked like they just didn't want to be out there at all. But I like Roy. I think he was a good appointment. They're a good young team with good young players and a proper team spirit. They look like they want to play."

More than this, the basic tone and texture of this England squad has shifted slightly. Joe Hart, Alex Oxlade-Chamberlain, Theo Walcott and Danny Welbeck seem to present a new hard core of genuinely agreeable young men, qualities evident not just anecdotally, or in their public appearances, but also on the pitch. There was something deeply endearing about Walcott's look of embarrassed delight after his goal against Sweden, which he later explained away by suggesting he did not want to waste time by celebrating and deflating his team-mates' momentum. Likeable enough for you?

The seeds of previous accumulated animosity pre-date even the Capello era. It was during the celebrified congealing under Sven-Goran Eriksson that England seemed to slip beyond the public sympathies, culminating in the orgiastic pomposities of Baden-Baden in 2006, a World Cup campaign of such overblown self-importance it seemed to poison the wells for a mini-generation. Why were England so disliked back then? Because they were dislikeable.

If that libidinal bond between fans and players has been cautiously reforged here, this is in part a beneficial effect of a general sweeping away. Of the old guard it is only really Steven Gerrard, John Terry and Ashley Cole who remain. Cole, it should be noted, is quietly venerated by many England fans who lack the imported venom of tribal Premier League allegiances. Perhaps the years have also been kind: as crimes go, having your private life raked over by the tabloid press, leading to the attendant public wronging of Cheryl Cole, is perhaps not quite as heinous as it once appeared.

It seems fair to say there is not so much blind hope as a sense of quietly renewed affection among manyEngland supporters in Donetsk. And England arrive at the Donbass Arena buoyed by a most unexpected ally: good vibes as opposed to bad vibes, an enhanced degree of understated appreciation, and the sense that, whatever happens on Tuesday night, they might still return home to a jarringly sympathetic welcome. In which case, Hodgson's England have already sprung one surprise at Euro 2012.