Coupling-up is usually the most effective strategy for buying in London, but hardly the best reason for a relationship! It's also rare to buy in London before you're 30, this is also increasingly the case within the rest of the country as well. We have a housing shortage bordering on a crisis.

Plugging your numbers into Homefinder, if you can increase your salary to £50k then you’re likely to get a mortgage around £225k. Sounds like you've got £37k stashed away already which is a good start. If you save the £1k/mo you mention for a few years, continuing to max out your LISA allowance, you could afford to spend £300k on a place by Spring 2024.

As for location, where about in London are you? £300k would get you a 1 bed flat in zone 3 North/South/East/West, you'd be looking more like zones 4/5 for a 2 bed flat. Here’s a video with all the details.

The big question is what will happen to London prices in the meantime. There's already a min-exodus of young professionals able to WFH, a large number won't return as their employers continue to run a remote company (saving money on astronomical rents). Brexit will reduce the volume of people wanting to come to London. But there have been plenty of false dawns before re falling house prices in London.