How about just taxing the profits of house sales exorbitantly? Eg 70% tax on profits of house sales unless you are a UK resident and it's your only home. This way it's still worth buying housing with the intention of leasing it, but buying housing just to sit on it will be drastically less profitably.
In the netherlands we have a saying: "Little house, little tree, little animal" (huisje, boompje, beestje). It means: Family life in a suburban home with a pet, a kid or two, a house with a garden, a car on the porch, a stable job, and the home is yours, you're paying off your mortgage, and you'll grow old with a nice nest egg in the form of having built up actual ownership, converting your salary into paying off the mortgage in the timespan of your career.
That's one kind of home owner. Of particular note is that at least in The Netherlands, and I bet in the UK too, the government likes this image. Most citizens do too. So, there are tax breaks for paying off mortgages and such.
The other kind buys as many houses as they can, converts it to crappy rent and because the dream, and the government's policies, are somehow trying to marry the mutually exclusive notions of 'anybody should be able to afford a starter house' and 'all houses should be good investments, giving you more return than just sticking that money in a bank someplace', rent is really high because the competition of just buying a house is really expensive too.
I bet that it is politically virtually impossible to attempt to deal a blow to the 'huisje, boompje, beestje' owners even if it makes perfect socio-economic sense.
So, seeing that as a political impossibility, you're looking for a way to somehow tax only the second category and also doing it in a way that lobbyers of the second category can't misconstrue your plan to get the first category on board.
I bet this is extremely hard to do: It's all one market, after all. If the second category is taxed into oblivion, their demand will cease to exist, which means house prices, also the house prices of the 'huisje boompje beestje' folks will fall drastically. This will do excellent things to the affordability of rent, but it makes those career folks edgy, to say the least.
It'll take quite a while for sufficient generational turnover (and 'the youths' need to vote A LOT more. Even if it does not matter at all; politicians are incentivised to chase policies that benefit those who vote) for me to believe any law that will screw over HBB folk is going to pass.
Your final sentence seems to assume that the youth don't want what you're calling a "HBB" life.
They may not be able to achieve it, but if anything, I'd think that they're more likely to vote in favour of it.
I'm young. Effectively since high school I've been working towards that life. It's what I consider to be a good, successful life. Relaxing in front of the fire or kicking about in the garden with the kids.
In the UK we don't have the American exurb life for the most part, but a little terraced house with a garden on a quiet street - sign me up.
There is nothing impossible about this unless you expect that an infinite number of people should pile into one city regardless of economic viability.
The second type usually uses a BTL (buy to let) mortgage, which can be interest-only and feasible where an occupier's mortgage wouldn't be. The UK government has successfully made these considerably less appealing, such as cutting tax relief on BTL mortgage payments. The housing was released into the better parts of the housing market.
