The next step would be to require that those that do not meet the rules sell up, which should put a bit of supply into the market and achieve some meaningful price movement.
Another good step would be to finally bring in a decent capital gains tax, ideally charged annually on paper profits at whatever your marginal tax rate is, and with no family home exemptions. Ironically taxing the family home would, in this case, actually make them more affordable by exerting further pressure to move speculators out of the market.