Find a cost neutral way to build more social housing for working people on low incomes. If less money going on rent then more money to pay the other bills
I agree - reducing housing costs would be the ultimate goal to reduce COL. Ideally, the average house should be able to be affordable on one average salary. This would also reduce childcare costs for a lot of families, as both parents could afford to drop hours rather than needing two full time wages, or have a SAHP if preferred.
In the short term, and where UC housing benefit is being paid, compulsory purchase of properties from landlords to convert into social housing.
In the longer term, I agree more social housing needs to be built. Perhaps couple with a scheme where there are incentives for under-25s to be employed to help build them, getting them work experience and teaching them valuable skills.
Also look at the private rental market to see how / if the private sector could provide a secure alternative to social housing for middle or higher income earners, who may not want or be able to afford to buy but want a stable home. Perhaps encourage big pension funds to branch out into this.