We absolutely can't do this easily. There is a reason why successive governments haven't done this.
Fundamentally a lot of this comes down to the fact that building houses is expensive, ties up a lot of capital and is practically quite difficult to do in terms of planning, infrastructure etc.
Think about it this way. If you are the government right now, if you want to fund a load of social housing then you are going to have to borrow lots of money. Obviously there is a huge risk that the markets simply won't lend it to you, but if they do then it's going to come with interest attached of around 5% at the moment if you look at Bond rates.
The average house built as part of social housing currently costs the government £160k. So each and every year the government will be paying £8k a year in interest on the cost of the building the house whilst the average social housing rent is only £4k. Add on all the costs of maintaing the property and you will soon see that social housing is hugely expensive. Remember whilst making these interest payments the government wouldn't actually be repaying any of the original cost of the property but just servicing the debt.
Social housing is absolutely not always better deal for the state than private renting using other people's capital to pay for the properties.