I would have said "tax whatever behavior you want to discourage":
1. tax unoccupied houses as punishingly as you'd tax pot or alcohol; in touristic places, such as Tahiti and Thailand, they went even further and outlawed land ownership for non-citizens; otherwise, they'd be covered with ultra-luxury villas occupied one month per year.
2. tax resale profits heavily as well: you do not want the competition of investors who might not even bother to rent their investment.
3. if you want people to own their place, tax landlord benefits aggressively enough, so that they'd rather invest on other financial products. But I don't think you want that: there are many useful jobs which don't pay enough to buy a house in a capital city.
4. raise interest rates. Or more realistically, introduce fiscal measures which simulate higher interest rates on mortgages, instead of simulating lower ones through tax breaks. Beyond a certain number of years, a mortgage doesn't make sense anymore, as you pay back interests only during additional years, no principal. This "certain number of years" is determined by the effective interest rate. Encouraging longer mortgages is encouraging higher prices.
5. review the welfare housing system. In many places, and I seem to believe London is one of them, you have market housing for wealthy people, council housing for poor people, and nothing in between for middle classes. There's no interest in building a city with only super-rich and super-poor people.
6. create tax incentives to encourage companies to move their HQ at least 25km out of center city, so that their employees will consider moving in the suburbs. Try to encourage the first movers to move to a couple of concerted locations, so that new centers reach a critical level of attractiveness, to carry shops and services with them.