I am struggling to understand why The Councils will not be able to borrow / repay to finance this, when surely this is exactly what the Labour Party have said they will do.
First of all, there is a difference between a government, which is able to control the supply of money in the economy, and a local council which exists partly on money raised by council tax and partly by money doled out to it by the government. The local council is like a household. It has a finite (i.e. limited) amount of money to spend. If it borrows it has to repay and if its income is static (or even reduced by central government cuts) and every penny of it is being spent on running essential services where is it going to find the money to repay what it has borrowed, or even the interest on what it has borrowed?
Whereas the central government has no need to borrow any money (it is not a household and doesn't have a finite amount of money), it can increase the amount of money in the economy at will and by whatever quantity it likes. So central government could, if it so wished, increase the grant to local councils so that they can build more council housing. Which is what Labour plans, I believe.