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I don't think the free movement of people/bankers is the issue with the City's objections. I think it's the passport / access to European markets.
The barrier to banks / finance companies moving stuff to other countries if necessary seems very low, and they can do it very fast. Like any international company, I don't think they'll feel particularly loyal to the UK if they can get a better deal elsewhere..
edit: it's not even a matter of loyalty, they won't be able to function properly from the uk...
"The financial services industry of the United Kingdom ... employed around 1.2 million people in the third quarter of 2012 (around 4% of the British workforce).
The estimated amount of total taxes paid by the Financial Services Sector in the year to 31 March 2012 is £63bn, 11.6% of the total UK government tax receipts."
You'd think employing 1.2m (more than the NHS employs) and accounting for +10% of tax receipts would be something the government want. But no, not in this age.