That is an extremely high salary, and very far from the minimum required to buy, even on your own. A dual £350k income is truly astonishing. You could buy most houses in London in cash after saving for 5 years.
First, you'll take home slightly over half of that net of various taxes and deductions, but let's be generous and say your take-home is 200k. You live very frugally, don't go out, don't really buy anything and keep your costs at 50k a year, including rent (!). That leaves you with 150k a year, so after 5 years you have 750k. This allows you to buy a modest 2-3 bed row house with a postage stamp sized garden in one of the less desirable areas of the city.
If you want something that doesn't look like a shed, you are looking at 1 million pounds and up, more like 1.5 million. If you want in a nice area and large garden, make it 2 million.
The only thing I can think of that would even come close to making a difference is having children. Then all bets are off, they can cost as much as you like.
'Inner London' and it goes up to £876K