At the moment, a range of Financial Services businesses such as banks, insurance companies and asset managers are able to operate across the EU as long as they have a base in the UK. This is known as passporting.
However, if Brexit occurs, passporting into the EU from the UK would not be possible unless special arrangements are put in place. Banks from outside the EU would no longer be free to just set up in the London and gain access to the wider market in the EU. To continue to maintain operations across Europe they would need to set up subsidiaries across mainland Europe in places like France, Germany, Amsterdam and Dublin, potentially, so those cities would actually benefit from taking away financial services from the UK.
Currently English law is the preferred choice of governing law for banking documents and transactions. However if the UK comes out of the EU, English Law would then be a non-EU Law and this would have an impact because from 1 January a new directive came into force -- the EU Bank Recovery and Resolution Directive -- which requires EU firms and certain in-scope entities, which would include EU incorporated financial institutions, to include a contractual recognition clause allowing them to recognise the bailing powers of the European Union.
This clause needs to go into non-EU governed contracts and obviously if English law is considered non-EU law, a lot of contracts would require this clause to be negotiated by both sets of counterparties so this would add to the cost of negotiations and the length of time it takes to actually agree the documents. The other problem with Article 55 is that the scope of it and the parameters are very vague and no one is actually sure which entities they apply to, and there are issues around how actually people are meant to comply, so this adds an extra layer to the complexity of transactions and documentation. A way to avoid all of this would be to have the contract governed by the law of an EU country. Now if the UK was not an EU country, English law would be less palatable than French law, Italian Law, Spanish Law and German Law so actually the dominance of English law in financial transactions would significantly diminish.