I live in London. Unfortunately, as the calculator shows, change in house prices is overwhelmingly the most important consideration in buying if you're thinking of staying for much more than 2-3 years. Admittedly growth is completely unpredictable, (and also highly inequitable), but to a large extent a decision to buy is based on expected future house prices.
For instance, I have a friend who bought three years ago - a £250k flat which would cost around £1,300 to rent. According to Rightmove and Zoopla (and the price a similar flat next door sold for recently), the monthly gain in value has been around £3,000 (!!). I also note this gain is tax free, so equates to earning more like £5,000 a month pre tax.
Unfortunately these gains are only available to those who earn enough and save enough for a deposit, or more commonly, those who receive parental assistance in purchasing property.
I noticed that one of the biggest factors, unsurprisingly, is Home Price Growth Rate and rent price growth rates. Do you have any sources for the rates historically? Preferably by location.