You won't find a house for £500,000 in London; you might be able to afford a 2-bedroom flat depending on where you're willing to live.
Your budget doesn't stretch to rich areas.
There are schools throughout London; likewise there are gyms throughout London.
500k not much for a house in a good area....!! Would not even get a studio flat in the best areas for that money..OBSCENE, I KNOW!!! I sold a studio, in a decent inner suburb of London, and bought a lovely, Victorian family home in a good area of MANCHESTER, for the same money...Vast swathes of Greater London are no longer for us ordinary working people....
500k will get you a one-bedroom flat in a wealthy or upper middle class area, not a house
st johns wood, ohhh forgot to say u need to have millions to buy a flat there