From what I've heard and read from others, getting a decent place at an affordable rent mostly is a problem limited to the inner-city boroughs. Croydon for example is quite affordable and well-connected in terms of public transport (20 minutes to Victoria or Waterloo).
Croydon is unusual, since those trains (actually to Victoria or London Bridge) run all night. A monthly pass is £210 though (zones 1-5), compared to £123 (zones 1-2) for nearer the centre [1].
In most other outer boroughs, getting home after midnight is either very expensive (taxi/minicab, including Uber) or very slow (two or more night buses). Most people I know -- in their 20s -- prefer a shared house closer to the centre.
All this will change in September, when (if?) the night tube starts running on Friday and Saturday nights.
Night bus coverage out to the limits of the tube is pretty good (e.g. I used to live on the Harringay ladder and the N29 runs direct from central London; honestly I'm not sure the night tube would make getting there at night any quicker, since it's right where St Ann's Road (Green Lanes) station on the Picadilly line isn't. The night bus to where I currently live goes all the way out to Enfield.
It's often not too bad if you're leaving from Soho, but redevelopment has pushed lots of entertainment out of Soho, so I'm likely to be starting my journey home from Camden, Islington, Shoreditch or Waterloo.
If the tube ran at night, I could reasonably stay out late in Zone 4+! I can't remember the last time I did that. (Why might I want to? Because people live there, and have BBQs etc.)
Indeed, and you hear these kinds of suggestions all the time.
It sums up the absurdity of the situation when it's genuinely and routinely proposed that a solution to ridiculous cost of living in a city is to live.. not in the city.
I travelled to Croydon a couple of times recently and it was never just 20 minutes. The trains are hardly ever on time. Also, "quite affordable" still means around £900 for a 1 bed flat + another £110 or so for council tax.