There are a number of potential reasons why the UK banking system has become so big. These include: benefits to clustering in financial hubs; having a comparative advantage in international banking services; and historical factors. It may also reflect past implicit government subsidies.
Evidence from the recent global financial crisis suggests that bigger banking systems are not associated with lower output growth and that banking system size was not a good predictor of the crisis (after controlling for other factors). On the other hand, larger banking systems may impose higher direct fiscal costs on governments in crises.
Source: Bank of England
In other words: the British banking system is large but stable, because the taxpayer would take care in case of another crisis. Lovely.
However, I like this line in particular:
Moreover, further work is needed to improve our understanding of the drivers of the n-shaped relationship between the ratio of credit to GDP and economic growth and on the quantitative importance of agglomeration externalities in banking.
Translated to plain English: We know very little, if anything.
This is just breathtaking—note the huge relative size of the British banking system compared to the US!