No, the financial industry has close to nothing to do with affordability in London. The main causes are the UK's cultural obsession with owning property, speculative property buying, and regulations put in place across successive governments to encourage property buying and keep house prices artificially high.

In the UK we historically associate wealth with land holdings and this has persisted to the present day. 'An Englishman's home is his castle' is long standing and famous adage that was at the core of Thatcher's economic reforms in the 1980's to increase home ownership amongst the UK population. One of her more famous policies was to allow people who were in social housing to be able to buy the properties that they lived in. This falls in line with Conservative policy and traditional ring-wing thinking that private ownership encourages positive, pro-social behaviour as you have a greater incentive to take care of things you own. To compound this further, average house prices are generally interpreted as barometer for the health of the economy.

You obviously don't want large swathes of the population to be upside down on their mortgage. But the wealth effect that occurs from increased house prices both on a household and on a nationwide policy level is largely illusory as the value generated is, for the most part, totally inaccessible. Homes are quite personal assets and to craft policy as if they simple financial instruments is misguided.

The UK government's staunch commitment to keep house prices in the UK is such that the barriers for foreign investment to buy property in the UK is almost non-existent. London's property market is basically the biggest money laundering scheme in the world. The UK government has passed some legislation to curb this activity but it is by and large just for show. This puts pressure on domestic property buyers as they now have to compete with foreign speculative/dirty money for the same supply of housing, driving prices up.

Plus, governments over the years have been hell bent on increasing home ownership as a policy (for God knows what reason). So they have instituted schemes to subsidise buying houses (which as far as I am aware have been discontinued for the most part). This only serves to push the price of housing up even further with a subsidy of the taxpayer, which makes absolutely no sense to me.

If prices were to ever fall drastically, this would be considered on the whole a failure of the incumbent government, which is why governments try everything they can to push prices in the opposite direction. This is despite the fact that a fall in rents would be the best thing that could happen for enterprise as it would make it so much cheaper for business. Now, the problem is that everyone is so attached to the value of property that if a dramatic fall were to occur this would likely destroy commercial and consumer confidence in the UK. But if you think about it, it is quite insane that the price of property has such a stranglehold on UK economic perception as it does not (directly) affect output of the UK economy whatsoever (except for real estate sales). Despite what I have just said, the fact that a large amount of households would end up in negative equity would be devastating to so many that the UK is essentially trapped in this cycle. So we are heavily invested in keeping the world's dullest ponzi scheme alive and well, and this will likely not change for a very long time.

So no, financial operations moving out of the City will likely not have such a big affect as to push prices low enough for lower earners to move back into central-ish London.

EDIT: I should also add that despite the recency of my arguments, increased property prices in London is nothing new. The average house price for London has doubled every decade since the 1900. I guess my point is, successive governments have essentially stoked the fire to the point where it is out of control and the only way to stop the fire from burning out is to keep stoking it even more.