At a time when globalisation, migration and terrorism are challenging traditional concepts of identity and nationhood, how can we develop shared values and common purposes? And what is the role of our cultural institutions in that endeavour?

There is no doubt that talking about Britishness and about the role of culture in integration has traditionally meant different things for each end of the political spectrum. For the right, it has often been about identifying a set form of history or cultural expression that people must sign-up to in order to truly belong. What some people will recognise as the infamous "cricket test". For the left, it has often been about allowing individual communities to express their own cultural identity, without striving for a sense of collective cultural belonging.

But both of those approaches have left too many people behind.

If we believe that integration, not assimilation, and community cohesion, not separatism, are vital to forming nations and neighbourhoods that are at ease with themselves, then we have to ask ourselves what are we expecting people to integrate into or express cohesion with? Finding a shared sense of common cultural identity is a key part of answering that question and it is right that we think about the government's role in helping people to shape that identity.

As a government, we have talked about a possible British statement of values. We are already better at making more of ceremonies for new British citizens, making use of town halls and other civic buildings. But I want to see our cultural institutions playing a fuller part. We have some of the best and most impressive spaces in the country - museums, galleries, theatres, libraries, historic houses and castles. Being made a British citizen in those kind of surroundings allows people to associate their new citizenship with key cultural icons, and then offers the chance to build a longer-term engagement.

The bicentenary of the abolition of the slave trade showed what could be done to bring people together around key historic events. I want see what more we can do to celebrate the key events that made us who we are. For example, the Charles Darwin celebrations next year. Yes, it is an opportunity to celebrate one of the greatest ideas of the modern age, but I also want to see if we can use the occasion to build an even bolder sense of our shared past and common future.

Next year will also see the anniversary of Henry VIII's accession to the throne. Given some of the less savoury parts of his reign, it's not an obviously straightforward event to commemorate. But understanding his reign is essential to understanding England. He is an iconic figure, a well-known personality in our history. And whether in separating state and religion, or in instituting English as the common language, or in being the first to clearly define and map our boundaries, a deeper understanding of his reign may help the important debate on England that is emerging.

Beyond that, we have the 800th anniversary of the Magna Carta in 2015, when we have the opportunity to acknowledge the beginning of the process that led to the rights and responsibilities that we take for granted today. I know that the British Library will have Magna Carta at the heart of the "Taking Liberties" exhibition this autumn and I hope this will be a chance to judge people's appetite for more.

But, all too often, our institutions aren't at their best when embodying common belongings themselves. The audiences for many of our greatest cultural events - I'm thinking in particular of the Proms - are still a long way from demonstrating that people from different backgrounds feel at ease in being part of this. I know that this isn't about making every audience completely representative, but if we claim great things for our cultural sectors in terms of their power to bring people together, then we have a right to expect that they will do that wherever they can.

I know that many organisations have made great strides, but there is much further to go.

This is an edited excerpt of the speech Margaret Hodge delivered to an Institute for Public Policy Research event on March 4. To read the full text, go here; also available as an audio file here.