I've known a lot of people in your position, op. In practically every case, people have either moved out of London entirely or moved to far cheaper areas.
I am your age and of the people I knew in London 20 years ago (I lived there for 15 years), there's only a handful left in the capital. Even Londoners born and bred with families going back generations in the capital, now live in other parts of the country, other countries or out in Kent. Dh, a Londoner, moved up to my home town in the North because we knew it was the only way we'd ever be able to afford our own home.
There seem to be three life assessment points: trying to buy a house, deciding on a primary school and choosing a secondary school.
I think you have to bite the bullet, roll up your sleeves, and be hardheaded and realistic about your situation. It's a good time to start thinking about a move to coincide with your DD's transition to secondary, and I would start with assessing whether you could do your job in another part of the country. £50k goes a long way outside of the South East, even if you take a hit of the loss of London weighting. £30k is a very reasonable salary in many parts of the country, and with your DP earning nmw, you would be able to afford to buy somewhere to live in a decent area if you did your research and played your cards right.
Realistically, you are not going to get social housing in London when you retire. In fact, I would not rely on there being any help of that kind in twenty plus years. Being older and skint in London is not a good idea, even if you own your own home by that time. I've retired in-laws in a financially-reduced situation in greater London and, even though they own a home outright, it's not a good scenario from a quality of life perspective.
I would seriously look to move. Okay, you'll never replicate the London life you have elsewhere, but ask yourself how much you benefit from your location on a regular basis anyway outside of work access. And you can build another life elsewhere that may be just as fulfilling. Different, yes, but just as valuable.
I would think twice about buying somewhere to let outside of London while remaining in the capital. It could be a whole heap of stress and you'd be relying on rental agents to manage the property for you for years.