The warm glow of Team GB's best performance in 104 years and pride in an Olympic Games well received at home and abroad have led a clear majority of the British public to conclude the £9bn they cost is good value for money.

A new Guardian/ICM poll has revealed that 55% of Britons say the Games are "well worth" the investment because they are doing a valuable job in cheering the country during hard times, outnumbering the 35% who regard them as a costly distraction from serious economic problems.

The commanding 20 percentage point lead comes despite the fact that respondents were expressly reminded of the cost in the survey, and may indicate faith in a beneficial legacy from the Games.

The findings appear to support the thesis of Lord Coe, chairman of the London 2012 organising committee (Locog), that enthusiasm for the Games would be a "slow burn" but would eventually ignite among the British public. Coe will also be cheered that support for the Games, which have the motto "inspire a generation", is strongest among the young and remains high outside the capital.

The performances of Team GB athletes, who have surpassed their Beijing total and are now guaranteed to finish third in the medal table, also appear to have helped shift public opinion, which was previously sceptical about the value of the Games.

Coe said there was a "limited window of opportunity" to capitalise on the feelgood factor around the Games and create a lasting sporting and economic legacy.

The debate continued to rage on Friday, with David Cameron defending the decision to abandon pledges around the amount of time spent on sport in school, and Labour's Ed Miliband calling for a 10-year cross-party plan to maximise the Olympic effect.

A total of £9.3bn in public, lottery and council tax funding was spent on venues and security, although ministers have said there should be about £300m in contingency money left over. Locog's £2bn operational budget is privately raised from sponsorship and ticket sales.

But hopes that the Games might foster a new spirit of tolerance towards migrants and minorities have met with more mixed results.

Coe has emphasised London's "home from home" welcome ever since London won the bid to host the Games in 2005, stressing the capital's tolerant, diverse nature. The public emphatically sides with Danny Boyle – whose opening ceremony celebrated symbols of diversity and declared "This is For Everyone!" – over the Conservative MP Aidan Burley, who infamously tweeted that his efforts were "multicultural crap".

By a two-to-one margin of 68% to 32%, respondents agree that modern Britain is stronger as a country of many cultures, support for multiculturalism that rises to 79% in London and 81% among the very youngest respondents, aged 18-24.

On the other hand, after being reminded of the success of minority ethnic Britons such as the Somali-born 10,000m champion, Mo Farah, voters remain inclined to doubt that most newcomers do anything positive for Britain.

By a narrow 53%-47% margin, the survey finds agreement for the suggestion that "More often than not immigrants … do not bring anything positive, and the likes of the Olympic-winning athletes are an exception".

Faith in the contribution of immigrants is much stronger in London, where 62% disagree with this statement, and a majority of respondents aged under 45 likewise disagree, but among pensioners there are particularly marked doubts about newcomers – with 64% of the over-65s describing the Olympians as "exceptions".

Attitudes harden further when the question switches to immigration in general. Only 32% of respondents say the Olympic successes make them "more positive (or less worried)" about it, against just 68% who disagree.

This time the refusal to allow the Olympics to alter attitudes is marked in every part of the country, including London, as well as across all age groups and regions.

Professor Anthony Heath of Oxford University, who has just completed a major study on multicultural Britain for the Economics and Social Research Council, said he was not surprised by the divergent results from the different polling questions. He explained: "We see an impressive level of support for multicultural Britain, despite continuing concern about immigration.

"That suggests the British public is rather more sophisticated than politicians recognise. Anxiety about the unplanned wave of immigration following EU enlargement is perfectly consistent with pride in the achievements of our long-established Black British and Asian communities".

Overall support for the Olympics is striking evenly split across the sexes, with 54% of men and 56% of women regarding the Games as "well worth" the cost.

Across the age range, the young are most enthusiastic, with support at 60% or more among the under-35s. The professional AB social class is keenest, with 63% saying the Games are well worth it, but among all occupational grades the enthusiasts outnumber the sceptics.

That is also true across every part of the country, except for Scotland, where opinion is evenly split 42%-42%.

London 2012 organisers will be particularly gratified that the triumphs of Team GB have translated into acclaim for the Games beyond the capital. They believe that the success of the torch relay, which was seen by an estimated 15m people on its 70-day tour of the UK, helped catalyse support beyond London. The enthusiasm of Londoners, 57% who see the Olympics as valuable, is in fact outdone by support of 58% in the south-west, 61% in the rest of the south-east and 68% in Wales.

Other surveys have also suggested that the Games have acquired a feelgood factor since they got under way. YouGov recently found that hosting the Olympics was the right thing to do by 57% to 29%, as compared to a 53%-35% split before the Games started. The 60% YouGov recorded as expecting a successful games before they started rose to 71% once they began.

ICM Research interviewed 2,021 adults aged 18+ online on 8-9 August 2012. Interviews were conducted across the country and results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.