The 2011 census data shows that the UK is much more diverse than it was 10 years ago (although this data covers only England and Wales). London remains the UK's most diverse place, with more than a third of its population born outside the UK, and only 45% describing themselves as white British. But only 45% of people in Leicester describe themselves as white British, 53% in Birmingham and 59% in Manchester. Even in parts of the UK that are still overwhelmingly white and British, change is happening fast – for example the ethnic minority population of Wales has doubled from 2% to 4% since 2001.

The census data confirms that the UK has experienced very rapid population change due to migration in the last decade: there are nearly 3 million more foreign-born residents than there were in 2001. Some parts of the country have experienced particularly rapid rates of population change due to migration: Wales, Yorkshire and the Humber and the East Midlands have all seen their foreign-born population increase by more than 75% since 2001, for example.

All this said, the census data won't contain much that would surprise most people in the UK – these changes happen all around us, all the time, and most people are just getting on with their lives. Only a small minority of people think that immigration is a problem in their community, although a large majority see it as a problem at the national level. New polling published today by British Future also confirms that people in the UK are much more at ease with our multi-ethnic population than they once were – with only 15% of people reporting that they are concerned about mixed-race relationships, for example.

Local problems, where they exist, are important – the census data illustrates a number of practical policy challenges: how to fund and adapt local services when populations change rapidly; how to provide services appropriate to the needs of diverse groups without creating unfairness; and how to support the small minority of people who don't speak English (4% of households have no adult who speak English as their main language according to the census, although many of these people will be proficient in English). Local communities need to come up with their own answers to these questions, something that will require both further devolution of powers from the national level and strong local leadership – integration is, in the end, something that happens in everyday life.

However, the national political conversation is important too. The census data shows that some of the assumptions made by politicians about identity and citizenship no longer hold – people have multiple and complex identities. An approach to citizenship that starts and ends with a test on British laws (and soon Shakespeare, Winston Churchill and Florence Nightingale) is no longer fit for purpose. New practical approaches are needed at local level, but we also need a new political narrative about who we are as a country – something that is challenging for both the left and the right.

In many people's eyes this census data is a record of Labour's failure – the UK population has been fundamentally changed by immigration that largely took place under the last Labour government, and which was opposed by a large majority of voters. Labour's challenge is to show that it understands people's legitimate concerns, without being dragged into unworkable populist policies or dog-whistle politics.

For the Conservatives, the challenge of the census is how to become more at ease with diversity – a new generation of Tories are comfortable with multi-ethnic, diverse Britain, but much of the party is not, and ethnic minority voters remain, on the whole, loyal to Labour.

By definition, a census can only reflect back to us what we are. The changes in the UK population in the last 10 years are undoubtedly significant, and there have been both benefits and costs. Politicians and policymakers on all sides of the debate need to assess not only the balance of costs and benefits but also where they have fallen in order to inform future immigration policy, and the census data will help with that analysis.

But regardless of the immigration debate, the question for communities around the UK is what can be done in practical terms to respond to the trends shown by this data. For national politicians the question is how the political debate can be changed to catch up with the realities of life in the UK today.