As an example:-256,000 were in Public education (also known as private ed. for any Americans)
Sounds like a lot of Public Schools (US: Private Schools), but could be individual Private Tutors, suitably registered for VAT, etc.
Note that there are 3,119 schools (of all recorded types) in the whole of London (both inner and outer). Never mind, as this helps your figures.
Public education, not public schools - in addition to tutorage, online courses, language courses and so on.
Financial companies can employ far fewer people to move money than Transportation And Storage do to handle the necessary goods (I assume, rather than being a weird conjunction of mass-transit and posession archival) to support those moving the money. Some people think this a Good Thing™, while others do not.
Not just financial companies, all companies! Only companies that need employ any more than an accountant to move money are massive retailers and banks who are moving valuable physical assets, like money from stores or bullion that's being transferred. Saves a lot of money and makes a lot of money moving obsolete, leaving more capital to grow a company and employ people dedicated to the company's function. In regards to financial companies in particular a lot of their wealth (unless they specialize in Forex trading or something) will not even be thinking of wealth in terms of Sterling, or even money - seeking value. To this end they'll be trading stock in companies, precious minerals, gas, crude, currencies against one another, in regards to derivatives this employs far more people in moving things of real worth. My favourite is a project I hope succeeds - some enterprising individuals are attempting to create a stock exchange for fishing! One thing unique about the fishing industry in particular (well, near unique, it shares this quality with industries like flower farming) is that from harvest to sale, the product must be moved very quickly to the local market (because everyone who loves fish loves fish fresh), and so everything that can expand the scope and reliability of this = more fresh fish moved :
D
But I digress, never employ people to do useless things, employ them to do useful things.
But apart from some possible oddities (is Mining just an unrepresented element of its supercategory, or does that include Crossrail diggers/etc, not already in as Construction?), many of the workers in one field (e.g. Health) support those in all the others. Or those in none (Social Services)! Remove or diminish Finance, and there's knock-on in other fields. Especially the Real Estate one. And Social Services might increase recruiting.
Crossrail diggers would go in construction, and mining businesses aren't underrepresented because there are a lot fewer of them in the UK, but the few there are make tons of money.
Like these peeps who do everything from the mining to financing through to maintenance services:
"This includes feasibility and development studies; legal, advisory, accountancy, tax and audit services; risk management, project management, best practice, environmental, logistics, legacy management and closure-planning services and communications strategies."
Then there's overlap, like Dawnus in the gov.link, which is a Construction Company in the Mining Industry
Most all workers and businesses support one another in some way (I'll concede the dubious usefulness of social work hehe), that's the consequence of a highly developed economy, its successes are intertwined, its failures are intertwined. Removing Finance would cripple any country's economic growth that has a developed economy, only North Korea could get away without noticing :
P
This is not the same as a dependency upon Finance and Insurance, as Financial and Insurance businesses do not make up more than a marginal percentage of London's businesses (being 90,000 est. of >5m est.) but they are pretty integral towards the running of the local, national and international economy. Insurance, money moving, investment, trading - they're like lubricant to the economy, keeping things slick.
It'd be pretty neat to have some alternatives, cos it helps to have a shield against international depressions - it hurts here when it hurts in the USA for example, but what alternative is there? You can't really shield yourself from the world's worst influences without also depriving yourself of the world's bounty