London - How to invest my bonus?

Property always incurs a cost, it doesn't matter whether you rent or buy.

If you buy, you will pay interest instead of rent. Mortgage rates are now ~4.5%. A £500k mortgage will charge £22,250 interest p.a., which is not much cheaper than your current rent. 

After you pay off your mortgage, there will still be an opportunity cost. The capital invested in your home could be invested in the S&P 500. If the S&P returns ~7% p.a., and your home has rental yield of ~4% p.a., you are effectively giving up ~3% p.a. of capital returns.

Please also remember that we are at the peak of a historic housing cycle in a rising interest rate environment. If you buy today or in the near future with a big mortgage you could very likely see yourself in negative equity. This will leave you financially trapped in your home until the market recovers - not ideal if you are a young professional and value the flexibility of being able to move house quickly.

There are also fee and tax considerations:

• Buying a home in London will likely incur ~£10-30k of transaction fees and stamp duty. Depending on the size of your downpayment, as much as half of your out-of-pocket expense could go towards paying taxes and fees. All of this is 'throwing money out of the window'.
• There are no capital gains taxes on your primary residence. But secondary residences are subject to a more punitive capital gains rate of 28%. Rental income from buy-to-let properties is subject to income tax. This makes property generally less tax-efficient than equities.

I think you should put your savings into an index fund and wait until you are married with kids and 100% committed to settling down in a location before you consider buying.