“Few events have done more to rescue the Union Jack from racists and royalists alike”, chirped the Guardian’s post-Olympics editorial on Monday, offering a rather strange equivalance in an upbeat liberal misreading of the impact of London 2012 on national identity.

Yes, the Olympics had been characterized by “a generous mood and a flag to share”, as The Guardian went on to say, and it was a good thing that Danny Boyle’s opening ceremony had something of a Heineken effect in resonating with many more usually allergic to expressions of national pride. But Olympic Britain, in August, was not suddenly a different country from Jubilee Britain, in June. The Olympics have changed, for now at least, some ways that we think about the Union Jack, it has not done so entirely according to the Guardian’s dream republican script. The crowds, doubtless reflecting settled British support for a constitutional monarchy, were hardly likely to snatch the flag back from themselves. Instead, Team GB has now joined the Monarchy in a photo-finish for the strongest associations that the flag has for the public. This does seem to be an inclusive move, and it coincides with a fall in the number of people now seeing the Empire as having strong associations with the flag than just a few months ago.

• What does the Union Jack mean to you? 
• (% who associate a great deal or a fair amount)
• Monarchy 85% (+2)
• Team GB 84% (+10)
• Armed Forces 80% (+1)
• Pride and patriotism 79% (+1)
• Sacrifice in the world wars 62% (-4)
• Empire 54% (-9)
• Democracy and tolerance 52% (-1)
• Modern, diverse Britain 40% (+4)
• British pop music 36% (+1)
• Racism and extremism 15% (-)
• (YouGov for British Future, August 2012 (changes since April 2012)

British Future launched in January, asking the question “2012: what’s our story?”. Whether the Olympics have changed what the public think is explored in two new pieces of polling, from Ipsos-Mori and YouGov, which return to attitudes that British Future was studying last winter and spring. The earlier polling was carried out in November 2011 by Ipsos-Mori, reported in the Hopes and Fears report, and by YouGov in April, in our This Sceptred Isle report, looking at British, English, Scottish and Welsh identities on St George’s Day last year. A new report in early September will look at whether the post-Olympic mood might extend the idea of being “Team GB” beyond the sporting arena to the society that we share.

The results suggest that the reason that 2012 has been an inclusive year for British identity was precisely because it has not depended on forcing a choice between tradition and modernity, as if historic roots are an impediment to a shared future, but has offered a reconciliation of the two. 66% tell Ipsos-Mori that the Olympic opening ceremony “represented the best of traditional and modern Britain” with 12% disagreeing. That was a theme argued eloquently by Hugo Rifkind in The Times last week, though this generated disgruntled dissent from Peter Hitchens, blogged “well, my kind wasn’t represented and I’m not reconciled”.

This poll finding suggests that Hitchens’ view that the ceremony involved “telling people who were not part of the cultural revolution that they had lost” is not held by many “pro-tradition” Brits. The poll shows English attitudes towards the Union Jack fairly stable since the Spring, except for a 10-point rise for Team GB and a 9-point fall for Empire. But poll findings suggest that the Olympics might possibly have had a rather more dramatic effect in Wales, and probably a mildly positive effect for British identity in Scotland too.

This has to be a tentative finding, with caution necessary. The YouGov poll is a UK-wide sample of 1700 respondents, so single-digit changes in Scottish or Welsh results might simply reflect a margin or error of around 10 points, and the Ipsos-Mori poll one of 1015 UK-wide respondents. However, the Welsh association of the Union Jack with pride and patriotism has risen 15 points (to 83%), with Team GB up 20 points (to 91%), the armed forces up to 91% (+13) and the monarchy at 90% (+8). In each of these categories, the Welsh findings were as or more positive as those of English respondents in the YouGov poll. YouGov found an 18 point gap between the score for pride and patriotism in the Welsh flag (86%) and the Union Jack (68%) among Welsh respondents in the April polling. Now, the Union Jack has had an Olympic bounce of 15 points among the Welsh, though we don't have an updated Welsh flag figure.

There were a number of anecdotal examples of this phenomenon in a BBC Wales phone-in – “are we all Team GB now?” (Iplayer) which I took part in last Monday. One caller, Mack, regaled presenter Jason Mohammed with the dramatic tale of how he, and each of his four brothers, had all had a Damascene conversion from recoiling at the Union Jack to being emotionally proud to be British throughout the Games every time another athlete won. He was retaining his republicanism though: “I wasn’t ready to sing God Save the Queen yet, but I was definitely humming it”, he said.

I wondered if he would feel differently when the Six Nations rugby returns to Cardiff, with the focus on Wales once more. There is absolutely no reason as to why British and Welsh patriotism need be a zero-sum game. A perhaps underrated feature of being British is that everyone has access to two flags, and can fly them both if they choose, as Welsh-British taekwondo gold medalist Jade Jones did on a victory lap of the arena. Scottish associations with Team GB rose 15 points to 80% and with the Monarchy by 14% to 94%, while the armed forces (78%) and general pride and patriotism (64%) both rose by 8 points, compared to four months earlier. That these changes are less dramatic than those in Wales partly reflects that three out of ten Scots consistently say say they are “Scottish, not British”, while six out of ten have a strong sense of British as well as Scottish identity.

The Ipsos-Mori polling on responses to the Olympics also paints a portrait of an inclusive and hopeful Olympic Britain. 67% of people say they are surprised by how much the Games have brought people together. No fewer than 75% say the Olympics “have shown Britain to be a confident, multi-ethnic society” with only 7% disagreeing. That attempts to create controversy about “plastic Brits” fell rather flat is reflected in a finding that 75% support all Team GB athletes equally, regardless of where they are born, while 13% say they do support British-born athletes more than those born outside the UK. Three times as many people say that events like the Olympics and the Jubilee bring people together (70%) as agree that they are a distraction from the real issues facing the country (22%). 82% believe the Olympics will increase how proud people are to be British, a view held by 83% of Welsh respondents and 73% of Scots, while 58% believe that the Olympics will leave a lasting, positive effect on British society. There is a good deal of immediate enthusiasm for emulating our Olympic athletes, with 79% of people saying they believe the Olympic effect will increase how much sport people play, and 50% believing we will see an increase in the amount of volunteering.

But most people don’t think the Olympics are going to determine whether Scotland is independent or not. Across the UK, 20% thought the Olympics would decrease the chances of Scottish independence, and 7% that it would increase it with 61% saying it will make no difference. Scottish respondents were more likely to say the Olympics would make Scottish independence less likely, with 33% saying it would make independence less likely, including 17% saying it would decrease support a lot (compared to 7% across the UK), though the small sample size means it would make sense to see if similar findings appear in future polls of the Scottish public.

Perhaps one reason for the positive national mood has been a rather different media agenda once the Games began. 64% of people say that the media tends to focus too much on the negative aspects of British society, while 12% disagree, while 65% say that British people don’t talk enough about Britain’s achievements.

Across the UK, 64% had expected the Olympics would boost the public mood when the year began. 86% said the Olympics has had a positive impact on the mood of the British public, while 6% say this has been negative, with 87% of respondents in Scotland and 88% in Wales saying the Olympics had been positive for the British mood.

Those findings show that people do want to work together for a shared society, and do have an inclusive sense of national identity. But to still be talking about “reclaiming the flag” from the far right misses the point. We did not need these Olympics to prove that you can be black and British, however happily the established fact was reinforced. If you want proof that those menacing “ain’t no black in the union jack” street slogans of the 1970s and ‘80s lost the argument long ago look at how even far right parties themselves have spent much of the last twenty years pretending and protesting that they are not racist anymore, for fear of alienating even their own target audience.

So there is no need to keep claiming that the collapsing, racist fringe elements somehow own our national symbols. Perhaps it is a comfortable rationalisation of liberal anxiety about national pride to think of this as rooted in concern for the ethnic minorities – but that depends on continuing to ignore the evidence about what most non-white Britons think with, if anything, slightly stronger feelings of British identity and pride than the white majority, on average. The confidence in the settled fact of Britain as a shared multi-ethnic society does not settle public controversies over what we now do about multiculturalism, integration or immigration. Those are simply not the type of questions that could ever be settled by a brilliant 10,000 metres last lap kick from Mo Farah. But we can have more confidence in our ability to address those issues together, after a summer in which we found that we rather like to like the country that we have become.