London could be justified in feeling a little unappreciated right now. Britons outside the capital think of its residents as “arrogant” and “insular”, an investigation by the Centre for London has found; London itself is seen as expensive and crowded. Pride in the capital decreases with distance from it, and appears to be declining over time. And while over three-quarters of Brits agree that London contributes to the national economy, just 16% feel it contributes to the economy where they live.

There is a long-held and persistent sense that London is too dominant in national life. Some also perceive its success as coming at the expense of the rest of the country – an idea that has re-emerged periodically throughout history, most famously in the 1820s when parliamentarian William Cobbett described the capital as a “Great Wen”, a gigantic cyst draining the life out of the rest of the nation.

Today, the capital’s appetite for investment in its infrastructure is seen as insatiable, serving only to strengthen the city’s magnetism, dragging talented young people out of the regions and into its grasp.

This idea seems to be on the rise, and the Guardian has just published a series entitled London Versus. But does this perception reflect reality?

The first thing to note is that the capital’s economy is seriously strong. With just 13% of the national population, London is responsible for 23% of the UK economy.

London’s 9 million residents live in the beating heart of an economically connected Wider South East mega-region (Greater London plus the south-east and east of England regions) of 22 million. The Wider South East is the only part of the country that runs a “fiscal surplus” with the rest of the nation – it contributes more in taxation than it receives in public expenditure.

Within the Wider South East, London’s surplus is particularly high: in 2016/17, the capital contributed £32.6bn more to the national purse than it took out. That money was then redistributed around the country, funding hospitals, schools and railways. If London was declared an independent country tomorrow, the rest of the nation would soon be bankrupt.

But the capital also receives a lot in return. In 2016/17, Greater London received the most public spending per head of any English region. Much of this comes in the form of capital investment, often involving highly visible infrastructure projects that can generate resentment and envy outside of the capital. Yet while London received the most investment per head, the south-east was the region that received the least. And who exactly is Crossrail for? Much investment of this kind may be in London, but is it really for Londoners alone?

Perhaps this is not the most useful way of looking at things. Londoners do not have an easy time of it, despite projects like Crossrail. In fact, the high cost of housing means the average Londoner is worse off than those elsewhere in the UK. And this is particularly true for those households with a below median income.

Child poverty rates in London are the highest of any English region or UK country, and this is expected to worsen in the coming years. And the capital has some of the most affluent but also some of the most deprived communities in the nation. Despite all the discussion since the EU referendum of the UK’s “left-behind towns”, poor Londoners are also at risk of being “forgotten”. Between 2009/10 and 2017/18, cities bore the brunt of local authority spending cuts, with London accounting for a disproportionate 30% of all cuts in Britain.

The Brexit vote revealed a divided nation. But these divisions were more complex than simply “London versus the rest” – and the solution does not lie in harming the capital’s success.

Ultimately, London plays a global role that no other UK city can rival. London is one of a small number of true “world cities”, competing with the likes of New York, Tokyo and Paris rather than Newport, Torquay and Preston. It attracts direct foreign investment that would otherwise head to another country, not another city. And these investments then have knock-on effects for jobs and further investments elsewhere in the UK.

London needs to get better at telling this story – and at ensuring that more is done to spread this investment and opportunity across the country. Regional growth need not be a zero-sum game – investing in Crossrail 2 should not mean a “Crossrail of the north” goes unbuilt. With its contribution to the national purse overwhelmingly spent elsewhere in the country, it is in London’s interests as much as anyone else’s that the UK’s other cities, towns and regions can thrive.

According to YouGov, most Britons outside London believe the capital gets more than its fair share of public spending. But it is reassuring that even those who held an unfavourable view of the capital conceded the nation was better off with London than without it. The challenge ahead is to ensure that London is seen as a unique asset, not a necessary evil.

London may feel like a different country to some people, but the UK and its capital have more in common than that which divides them. That includes a mutual interest in seeing the nation’s economy grow outside of London.

• Jack Brown is a research manager at Centre for London