And with the UK out of the EU, how is that different? Actually, it's far more likely to happen if we leave because the EU won't have a single financial powerhouse if London leaves...
The Eurozone just will not be happy to use London as the single financial powerhouse. It will want a powerful financial centre in the Eurozone, which will compete with London.
If we're out of the EU, and the Eurozone bring in stringent trading regulations that would impact our practices in the City, we would not be bound by them, any more than any other independent country. The City can continue to make money and be governed by City regulators and Parliament.