In short, no.
Modernising our current Stamp Duty on shares to get rid of loopholes and extend to a few more products would be a modest tax increase entirely affordable by a financial sector rich enough to reward their CEOs every year with multi-million pound pay packets.
Banks relocating because of the FTT doesn’t make sense. Given the UK already has an FTT on shares, if the strain of such a tax was really a deciding factor of the location of their business then finance firms would have relocated to Germany (where no FTT exists) years ago! The reality is that the FTT is just one of a number of costs of doing business and not high enough for a finance company to relocate its operations.
The real question is what would actually lead UK finance firms to relocate? To which the answer is if the outcome of Brexit negotiations does not give these companies sufficient (or sufficiently profitable) opportunity to do business with EU countries.
Finance firms have opportunistically seized on Brexit as an argument to prevent any moves to tax their sector more. Ultimately, what we cannot have is politicians using uncertainty over the Brexit outcome as a reason for delaying a fair, affordable and timely tax increase which is needed to ease the problems faced by many people across the UK as a result of the financial crisis the banks caused.