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Why London should secede from the UK in one chart

The imbalance between London and the rest of the U.K. has never been starker, and that disparity is widening.

Oliver Harvey, macro strategist at Deutsche Bank uses the chart below, which contrasts the economic output per person – what's called gross value added (GVA) per London resident with the rest of the U.K., to argue that London may be part of a "flawed currency union" with the rest of the U.K.

"In many ways the U.K. fares worse as a currency area than its largest trading partner, the euro zone, which is commonly criticized as an experiment in monetary union gone wrong. This is the result of the differences that exist between one U.K. region, London, and the rest of the country," Harvey wrote.

According to the graph below, the gap between the GVA per person in London and the rest of the U.K. has grown massively in 14 years. In 1997 the average Londoner's GVA was about 9,000 pounds ($14,000) while the rest of the UK's figure was about 4,000 pounds. But by 2011, the London figure was more than twice that of the rest if the UK's average – nearer 18,000 pounds compared with about 7,000 pounds.

London accounts for 13 percent of the GVA to the U.K. economy each year – in comparison, New York accounts for 7 percent of the U.S. GVA.

While the country's capital and its environs barely had a recession, with 12.5 percent growth between 2007-11, and house prices more than recovering from their credit crisis blip, the rest of the U.K. is in the doldrums. The average wage per hour for someone working in London in 2012 was £15.70, compared to £10.01 in Northern Ireland. And the current account gap between London and the rest of the U.K., because of London's comparative export strength, is greater than that of euro zone paymasters Germany and delinquent Greece.

There has been plenty of debate recently over whether Scotland should leave the U.K., but the question of whether London, essentially a creditor to the rest of the U.K., could leave is also being semi-seriously asked.

(Read more: Scottish independence: Widnae it work?)

The city's role as a financial center has helped it outstrip the rest of the U.K., and it is increasingly international, with around a third of its population from outside the U.K.

Of course, most developed economies have most of their wealth concentrated in cities. Yet Harvey's analysis suggests that the division is much greater between London and the U.K. than between the wealthiest regions in the euro zone and U.S., and the rest of their countries. It is even bigger than the division between the former West and East Germany.

During the last election campaign to become Mayor of London, runner-up candidate Ken Livingstone even said he would "declare independence" if elected.

(Read more: Zombies could cause spooky 'lost decade' in U.K.)

Removing London from the equation might give the rest of the U.K. more chance to set its own rules. After all, one of the key points the Scottish National Party is making in favor of independence is the London-centric nature of U.K. politics.

The real economic reasons London should stay as part of the U.K. are the mobility of workers and the importance of public sector work, funded by taxpayers, to the regions outside London, Harvey points out. Essentially, this means that much of the duller, lower-paid work needed to keep the engines of the country running can be done more cheaply outside the capital – which is why it may make sense to stay within the U.K.

- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.