I'd like to see rules brought in to force the banks to pass on the low interest rates to people looking to take on new mortgages. The BofE have interest rates set at 0.5% but mortgage rates offered right now are higher than when DP and I bought back in 2007 when the BofE rate was 5.5%.
I also think longer fixed term deals should be made available to more people, so that people can have some confidence about the size of their largest outgoing beyond the 2 year mark. For example, if you could get a mortgage rate of 2.5% with a 10% deposit on a 5 or 10 year fix (or longer, as available in some other countries) then the bottom end of the market would start moving again as first time buyers could afford mortgages again. This would start the entire chain up, including allowing pensioners to move out of their too large properties and into retirement properties, or at least smaller ones!
I know this doesn't fix the insane prices (particularly in the south east) but it would bring home ownership back into reach for some people and hopefully bring some rents down as there is reduced demand for rental properties.
I also think right to buy should be scrapped and the rules around duration of tenancy, inheritance of council property etc need to be overhauled. Council housing should be a safety net for people who cannot afford a home any other way.
I'd also like to see brownfield sites used more to build new housing, but minimum room sizes should be brought in, so that the houses built are actually fit for purpose (bedrooms must have space for a wardrobe etc), planning permission should be dependent on space/buildings being provided for GPs surgerys etc, perhaps contributions from the developers towards the cost of extended public transport services out to any new developments (this is already done to some extent in some areas with the requirement for public transport policies and action in new developments) and green space must be included within the development so that communities can develop. I also think these sites should have to have a range of housing; houses, flats, social housing etc and 3 social housing flats in a development of hundreds is not sufficient, it must be a meaningful amount.
Finally there are an insane number of empty properties in the UK; some abandoned, some owned as "investments" by the super rich. Rules on bringing these back into use should be strengthened to give councils more powers to repossess them.
In an ideal world I'd personally ban ownership of more than two properties (two to allow for (e.g.) people in rural areas to take jobs in towns/cities if needs be without losing their homes in the country) - I think buy to let landlords owning hundreds of properties are immoral; these are homes, not vehicles for profit. But no government will ever do this.
Also agree with comments upthread about improving tenants rights. If other european countries can manage this, then why can't we?