I don’t have your data, but I think you’re possibly conflating the effect of the 2008 collapse, and subsequent limitation of mortgages to first time buyers (who typically don’t have a deposit in the form of equity in a property they’re selling). The need to find a large deposit and the more rigid affordability requirements are huge handicaps for first time buyers.

While it isn’t true everywhere, the cost of a mortgage and the monthly cost of rent aren’t massively far apart, so with no deposit issue, most tenants could afford to pay a mortgage. So they’re either choosing not to, or they are unable to get a mortgage.

BTL grows to fill the demand from people who can afford to pay to live somewhere, but can’t find a deposit. It’s true that BTL landlord’s tend to favour exactly the properties that would appeal to a first time buyer, and that therefore that increases competition for properties. But I know lots of people who can’t afford to buy a property and none who can afford it and can’t find one (I don’t know anyone in London, to be fair).

Competition isn’t the main driver of house prices, it’s confidence. If it was simply an issue of supply and demand, house prices would be much higher and increasing faster, as demand increases and supply falls behind. House prices fell in 2009, and there was no change in the numbers of people in the country or any step change increase in the number of properties.