So, Just How Inefficient is Local Authority Housing Administration?

I can't find national statistics, so I will use the figures provided by my local council, which I guess is a reasonably good guide to the average.
The accounts include two different profit and loss accounts for their council housing, on pages vi and 38; total income is around £34 million and real cash expenses are around £18 million, including employee costs of £3.7 million. So unless more than half their income is from Housing Benefit, that's a nice little profit for the taxpayer.
It doesn't say how many people work in their housing department, but let's guess each employee costs £30,000 a year, so that's 125 employees. Neither does it say how many units of housing they look after, but let's call it 7,000 (£34 million divided by £100 a week rent).
So that means it one council employee looks after fifty-six homes. That includes managing the waiting list and allocating vacant ones; sorting out the repairs; collecting the rent and council tax; and administering housing-related benefits etc.
Ho hum.
------------------------------
How does that compare with the 'private' sector?
According to the ONS there are 422,000 estate and letting agents (construction is a quite separate category) and 1,285,000 people working in finance and insurance.
Let's assume that half of those working in finance and insurance are involved with mortgages and home insurance, this means that there are 1,450,000 people looking after 22 million or so privately owned homes.
That means on average, in the private sector, one worker looks after about fifteen homes.
Going by that simple measure, local authorities are nearly four times as efficient as the private sector.