Eighty per cent of Europe's hedge funds are currently based in London, but efforts are under way to tempt them to move to Switzerland.
A representative of eight Swiss cantonal governments will hold a meeting in a London hotel on Wednesday to try to convince hedge fund managers to leave the UK.
The Swiss initiative comes as changes in UK tax regulations, and EU plans to regulate hedge funds more tightly, are starting to make other locations look more attractive.
But how likely are they to leave?
One who has gone already is Karsten Schroeder, chairman of Amplitude Capital, who swapped his office in London for the small Swiss town of Zug 13 months ago.
As he steps out onto the balcony of his fifth-floor office, unable to miss the snow-covered mountain that frames most of his view, he says he has no regrets.
"We wanted to have a bit of a calmer life and also to spend more time outside instead of a big city life," he says.
"Switzerland had a good combination of both - this personal aspect, but also a country that has an infrastructure that allows you to operate a business in the financial services industry."
In total, eight people moved over from London to Zug to open Amplitude's new office, but the Swiss authorities hope they can persuade many more to come over from the UK.
At Wednesday's meeting in London, Marc Rudolf, head of the Greater Zurich Area - a marketing arm for eight local cantons - will make his pitch to other hedge fund managers.
Mr Rudolf will tell his audience that moving to Switzerland can significantly reduce an individual's tax liability.
"People have concerns about London, the uncertainty with taxation," he told the BBC.
"I often hear, 'We cannot plan our future, we never know what's going to come.' This is naturally a time of opportunity [for us]."
Switzerland is not in the same league as the UK when it comes to hedge funds.
A study in July 2009 by Eurohedge, a hedge fund information company, found that while there were 55 funds in London with at least $1bn under management, in Geneva there was only one.
But the Swiss hope recent changes in UK tax regulations will attract some new business.
The £30,000 tax on non-doms, combined with the new 50% tax rate for those earning more than £150,000, has led to unprecedented levels of interest in people leaving London, says Monica Cohen-Dumani, an international tax specialist with Price Waterhouse Coopers in Geneva.
"We do see an increase for a couple of months now, more requests, more questions coming in," she says.
"Every other day I will receive a question [from Britain] from someone, or one of my colleagues will receive a question [about how the tax system works in Switzerland]."
But turning that interest into action is proving elusive. So far, two hedge funds - Brevan Howard and Bluecrest Capital Management - have announced that they will help staff move to Geneva if they wish.
At the same time, brokers Tullet Prebon will expand their Swiss operations if some of their London staff, mainly commissioned-based traders, want to avoid the new tax rate by moving to Switzerland.
For many others, however, the likelihood of paying less tax is not enough.
"Switzerland is not for everyone," says Markus Federle, head of the Fairsky Group, which helps businesses relocate to Switzerland.
"The individual preferences of fund managers and those of their spouses play a fundamental role," he says.
"And there are a number of people who say they will not move to Switzerland, even if it saves them a lot of money.
"It is very often impossible to move the entire operation to Switzerland, because you will not be able to convince the entire team to move."
What is most likely to happen, says Mr Federle, is that the new taxation rules will encourage companies to open offices outside the UK, possibly in Switzerland, and structure their businesses in such a way as to reduce their tax liability.
That means there will be no wholesale emptying of the City, but the people who do leave will probably be the rich, the highest taxpayers.
So while their numbers may never reach a critical mass, the Treasury is very likely to notice their departure.