To illustrate the massive disparity in increase compared to the rest of the country, we bought a 2 bed terrace in Leeds in 1995 for £32k. It's now worth around £150k.
A 3 bed semi in a similar area (nice but not Mumsnet nice, the sort of area you might look at when you can't afford Horsforth or Chapel A or would prefer not to deal with the traffic if you need regular motorway access) would have been around £50-60k at the time and now around £250k.
Whereas London prices then would have been around double Leeds prices but are now more like 5-10 times more, so they've accelerated away disproportionately.
I think there was a lot of growth in London when there was price stagnation in the rest of the country, ie slower to increase again after the 2007 crash.
Here prices have only got back up past those levels in the last 3 years ish, whereas in London there seems to have been a lot of growth in the early 2010s.
But obviously deposits are much more of an issue these days. Pre 2007 100% mortgages were widely available for first time buyers or 5% max. Our deposit was £1600 and our mortgage gave us cashback that just about covered the fees.
Now, people often need higher percentage deposits, especially if they don't meet income multiples.
Stamp duty is probably also more. In the mid 90s you didn't pay any below £60k. I don't know what stamp duty is now, but if someone is buying a property that is modest by London standards, say £500k or so, they probably need a £25-50k deposit as a minimum, plus stamp duty and fees could make it more like £60-100k, or more if you are stretching the income multiple.