This paper examines whether EU membership enhances or diminishes the UK's financial sector stability, and therefore its prominence in global finance. The UK is host to the largest share of financial services in the EU, despite being outside of the Eurozone. An important reason is that, as a member of the EU, the UK has direct access to the Eurozone's financial infrastructure. If the UK leaves the EU (and EEA) banks and other financial services firms may continue to have access to the Single Market, but they are unlikely to have direct access to the Eurozone's infrastructure. Banks in the UK will no longer be direct members the Eurozone's payments system. The swap arrangement between the European Central Bank and Bank of England would have no legal enforcement mechanism. Resolution of cross-border banks would be more challenging with less incentive for a cooperative outcome. While some may welcome the reduced size of the financial system, not without reason, this could be achieved more effectively with domestic regulation than by leaving the EU. Given the uncertainty that would follow a vote to leave, there is a risk of capital flight.