What should be Britain’s role in the world in the 2020s and beyond? The question can’t be divorced in any meaningful way from the approaching general election. Few modern elections have been so clearly a search for national identity and meaning as the 2015 contest looks like being. But no election outcome will make much sense unless it simultaneously offers a new and consistent account of this nation’s place in the wider world.

Foreign affairs rarely play a prominent role in general elections. Yet 2015 ought to be an exception: partly because of the British relationship with the European Union, about which this election outcome will be so decisive; partly because this will be the parliament that decides whether to renew Trident, the ultimate embodiment in many eyes of great-power status; and partly because of the objectively greater sense of international tension that has followed the standoff with Russia in Ukraine, the rise of Islamic State (Isis) and the uncertainty in Europe embodied in the Greek election result.

By several measures, David Cameron’s Britain has stepped back from the active global and regional engagements favoured by most of his recent predecessors. Cameron has brought the troops back from Afghanistan, to general relief; has been compelled by public caution not to intervene in Syria; and has distanced Britain even further than his predecessors from the eurozone and its momentum on European integration.

True, he has at the same time bombed Libya, joined the conflict against Islamic State in Iraq, sent troops to west Africa against the Ebola threat and nurtured a better relationship with Angela Merkel’s Germany than Labour ever attempted. But he has also cut the defence budget – and will cut it further if re-elected – and, through the still unfinished Chilcot inquiry, he has kept open the space for fresh introspection about future UK military intervention. In sum, the Cameron-Clegg government has represented a brake on recent foreign policy trends but not a break with them.

Some have gone further, drawing the conclusion from the public mood of Cameron’s Britain that it is embarked on a journey into isolationism. The Syria vote was pivotal in this view of things. But the rise of Ukip, with its core aim of UK withdrawal from Europe, supported by a significant section of the Tory party, can be seen as a symptom and a cause of this isolationist mentality; while the rise of the Greens and the SNP, both opposed to Trident, could indicate a public mood that is more ready to step back from traditional military great-power aspirations. Anti-immigrant feeling increases the sense that modern Britain is minded to pull the duvet over its head.

But there’s a large problem with this thesis. It is not borne out by the facts. It is certainly not supported by a detailed new Chatham House analysis, based on surveys by YouGov. This not only discerns no public shift towards isolationism over the past five years, it also clearly identifies a growing, or perhaps a reviving, appetite for the UK to aspire to be a “great power” rather than accept its decline – 63% of the British public have this aspiration, the highest figure in such surveys since 2010. At the same time, however, 60% think that Britain is expected to do too much internationally, while 54% think Britain should spend less on aid.

This nuanced commitment to engagement is supported by answers to some of Chatham House’s more detailed questions. An even larger majority – 69% – think the UK has a responsibility to maintain international security; 58% think the UK should provide troops for peacekeeping missions; and 56% think it should help lead global responses to climate change.

Elsewhere public views are mixed. On Europe, opinion is evenly divided on whether to stay in (40%) or quit (39%). But more people (30%) now think the UK’s closest ties should be with the EU than with the US (25%). Though this survey did not ask about Trident, yet another YouGov survey for the Times has found only 25% in favour of full Trident replacement and another 25% opposed to any UK nuclear weapons, with 31% favouring a less powerful and less expensive replacement system.

This hardly adds up to a people in full retreat from global engagement. It may mean some parts of Britain in more active retreat from some forms of engagement. Support for the EU, for instance, is stronger in Scotland and London. This raises the interesting possibility that, if there is an out vote in an EU referendum, it won’t just be Scotland that may try to secede from Britain. It could logically even be London too.

What the Chatham House survey really shows is two things: first that Britain remains pretty realistic and sensible; second, that we need to do more to take the great out of Britain. Britain has a majority for global engagement, but not for doing more than is appropriate; for strong defences, but something less than full Trident renewal; for a continued role in, and close relationship with, the EU, but not closer integration on needless things; and for strong action on climate change and international epidemic threats, but less on aid spending. Britain’s natural allies, the survey suggests, are increasingly our northern European neighbours, while our biggest threats are from Russia and international terrorism.

You can pick holes with some of these mainstream positions. Most of them, however, seem extremely reasonable. Some of them are badly informed. You can argue, rightly, that far more needs to be done to puncture popular myths about Europe – the British public’s mean estimate of the UK’s net contribution to the EU budget, for example, is more than 10 times higher than the true figure. But the idea that this country is on a journey to isolationism just isn’t true. What it badly needs are better leaders to give stronger voice and clearer direction to the public’s own decent instincts.