iirc money mostly enters Britain because they use it as the way point for the tax havens "controlled" by Britain; their overseas territories and crown dependencies. Then it disappears into the land of political and financial voodoo of nameless holding companies, trusts and such, where nobody knows who is responsible for what, in both holdings and regulations. Mossack Fonseca's Panama Papers were a fairly big deal, but in reality that was the tiniest glimpse into that opaque world, and the revelation ended up changing nothing. Politicians still campaign about tax rates as if they mean anything when they can just be avoided.
I believe it is more the case that the banking sector in the City of London is the institution, and the secrecy jurisdictions are tools that it developed and uses. Historically money ended up in England because of the Eurodollar system, and from there banks use the secrecy jurisdictions to create trust systems across different jurisdictions for opaqueness. England as an intermediary is preferred because there is a level of trust there with their institutions that isn't there with some bank in a random backwater.
By random backwater I meant some random place that wasn't involved with the major colonial powers during that period. The reason most of the offshore tax havens are what they are is because they were remnants of colonial empire that could be exploited.
I think the path dependency is what made the City of London the hub, and their trust system is how non citizens were able to access their financial system and those in their territories as well. I'm sure now there are ways to access services in these places directly now, but historically, the majority of the infrastructure dedicated to this stuff in these places was built out from England.
