The geography is important. With the exception of Johannesburg, all of these cities were in a position to become logical naval trade hubs for regional distribution. Throughout the 18th and 19th centuries the UK was the dominant naval power in the world, and so it was in the strategic interest of the UK to build up and provide protection to these ports. Sometimes, as in the case of Hong Kong, they were built up from nothing, to provide a competitive alternative to an existing port (Macau), and sometimes the geography was just so favourable (Sydney Harbour) that whichever power dominated that area it would be the prime position for a naval base.

For one, not all of the above were purely British or administered in the same way. Johannesburg as an example was founded by Boers and ergo Dutch colonists. It would also be a stretch by any margin to call Dubai a British colony as the Trucial States were a protectorate, which the British never administered domestically.

To state that Britain was the only colonial administration to see its former colonies blossom in that way would also be rather inaccurate. Both Rio de Janeiro and Sao Paulo, ex-Portuguese colonies, are important financial hubs, as are many cities in the former Spanish domains. Other former colonies too have had success: we can hardly consider Kuala Lumpur a world financial center if we don't consider Jakarta first.

It is however undeniable that many former British colonies did indeed become important centers of trade. Part of that reason, as noted already by /u/ROBOTNIXONSHEAD, is the geostrategic location of many of your listed cities, such as Singapore and Hong Kong. I'd also add that of all the colonial powers, Britain by far controlled a much larger share of the world's population. Ceteris Paribus then, there would be more people requiring financial services in their territories than others. I think the core of the answer to the question lies here. Many British colonies were located at geostrategic locations, with good access to a heavily populated hinterland (Hong Kong and the Pearl River delta, Shanghai and the Yangtze, Calcutta and the Ganges, etc) at a time when world trade expanded massively. Often these cities grew even further due either direct British stimulation and investment (as in the case of Aden, Calcutta or Singapore) or a Port Treaty system that made it difficult for domestic cities to compete with western controlled settlements (as in Japan and China).

Nonetheless, I do think it is difficult in this case to make sweeping statements about the colonial British administration as many of the colonies were administered at different times, and in different ways. If any comparison were to be made, we would have to first define what qualifies as a colony (do temporary concessions such as Shanghai, Hong Kong or Macao count?) and what exactly could be counted as a purely British colony as opposed to one from a different nation (Is Cape Town British or Dutch, Shanghai British or mixed, New Orleans French or American, Mumbai Portuguese or British. etc). A post WWII look at this would most certainly be interesting, but we'd have to first narrow the scope quite a bit.

Montreal's (Quebec, colonial French settlement) exchange was larger than Toronto's until the 1920s, and was still quick strong until the FLQ crisis in the late 60s/early 70s. Arguably one of the main reasons for its decline is potentially the same reason why English language areas seem to be the current global financial centers -- language. That generates a chicken/egg problem though, because the reason the language became so dominant in finance is because the big exchanges were all using it.

Some historians, most notably Niall Ferguson in The Great Degeneration, but also economists from the Charter Cities movement, like Paul Romer, have argued that what the British did was export their way of doing things to their colonies -- parliamentary democracy, a legal system based on judicial precedent, the idea that "possession is nine-tenths of the law" -- as well as providing a stable, more or less impartial government and judicial system. These institutions are conducive to economic development and capitalism in other countries just as they have been in the United Kingdom. Except for the Dutch, no colonial power combined imperialism and capitalism like the British and the Dutch didn't colonize Indonesia as much as factory farm it, like the Congo Free State.

While the British didn't treat Indians, Chinese, Maylasians and Arabs as equals, they allowed them greater freedom and educational opportunities, a greater role in administration than the Africans -- and so they never got any of the benefits of Empire, just the costs.

These cities have also been major ports for years and have maintained their connections to London firms and markets.

I have an issue with your premise. How do you define financial centers? That would not be a list that I would select, and I'm a financial risk management consultant for large corporates. The current centers I would pick are NYC, London, Hong Kong, Singapore, and Tokyo.

Johannesburg was a Dutch (Afrikaaner) city until the English got their grubby mitts on it.

My theories:

1. Language, with english as linga franca.

2. Military power, making rading a port and looting the banks less attractive.

3. The english legal system, which is less crooked than other legal systems.

4. Along with 3, the House of Lords. They act as a sort of supreme court, so if something went sideways in a colony it can get fixed in London.

5. Along with 1, the english public boarding schools, along with oxbridge, means financial guys all over know each other.

6. Hong Kong and Singapore are also run by the formerly cantonese speaking Chinese diaspora, which is perhaps the brightest ethnic group on earth.