People can invest how they like. Stopping people have multiple properties is not going to solve the issue. There is not enough money to build all the social housing that some people seem to want.
Properties should not be left empty. If a property has been left empty for more than a year or is occupied for less than say 6 months out of 12 then either it should be sold or the Council can compulsorily purchased to get the property back into the market. That would stop holiday homes just used a few weeks out of the year, but would allow those with longer term rentals and holiday homes that are let and occupied a lot. That would free up housing.
Bring back more 95% and 100% mortgages, since deposits seem to be the big issue. If someone can afford to pay more than the mortgage amount in rent, it seems silly that they are told they do not earn enough to pay the mortgage.
Stop right to buy for Council housing. They are being sold at massive discounts and the money is not enough to replace the social housing. If they want to keep a right to buy type scheme or the ability to sell older Council homes to bring in newer stock, they should be at full market or slightly discounted prices, not where people can get up to 70% off.
On top of that, people need to take responsibility for themselves as well. I know too many people complaining that they cannot afford to buy with 2, 3 or more children so are stuck renting because they decided to have children first and cannot get social housing. That is fine if people choose that, but they need to own the choice they make as well and not always think it is the fault of those who have more than one house or the government. We get to choose our own priorities.