Why not nationalise mortgages, have one bank (the government) lending. Set interest rate (as it is anyway). Goverment mortgage bank is non profit so pays staff but not any shareholders. Any interest we pay on our mortages is put back into the economy to good use.
Un-sued vacant housing stock bought up by government and let out/sold. Profits put back into economy.
I'm in favour of the free market but too much weirdness is going on in the property market - with buy to let landlords able to borrow but first time buyers not.
Fat cats wouldn't like it.