For a 2019 purchase there is no way that’s more than a studio maybe maybe a tiny 1 bed, if I want to buy where I rent now (W2) I’m looking at 1M+ for any two bed that isn’t a 50sq/m lower ground closet, the non council is a given I don’t think there are any council properties in Soho…
The 2 bed flat I’m renting got recently evaluated at 1.7M it’s very nice and very large (for London)but the lease remaining on it is 68 years and the Victorian building it sits in would need a lot of work very very soon so the buyers are looking at 350-400K bill within a few years of buying the flat (leasehold renewal and building repairs) on top of that which also is why the current landlord is looking to sell.
As it stands now if you want to buy a property for £600K you are looking at £60K deposit, £20K stamp duty and probably another £20K for misc costs.
£600K is a below what an average new build in a Zone 3 would cost you these days outside of the few units they reserve for HTB. If you can save £3K a month you’re looking at 3 years of saving. Since most people / couples would struggle to save even £1K a month especially in their early careers they are probably looking at a decade of saving for a property or even more if the house prices keep on rising as fast as they are now.