You'll probably find that faith schools are given special treatment. Blair and Cameron both terribly keen. They are already, in effect, a kind of academy, with the religious organisation being the "sponsor".
In middle-class areas the governors with special skills tend to come from... the parent body. People with a managerial or professional background are certainly needed if the GB is to be anything other than a box ticking chore for the head. One of the biggest contributions I used to make was in HR as the Head had little training in this area, and many tricky issues to deal with. The first head I worked with, when asked "Where are your personnel policies" looked around his office in bemusement and then pointed to a row of dusty lever-arch files and said he supposed they were them. The next head was rather impulsive and many times I said to him "Have you read the policy ? It's there to cover your arse as well as protect the staff member. Now follow it to the letter"
My knowledge was also handy on the two occasions when I had to chair an appeal panel (we sacked 2 teachers - a big deal for a bunch of volunteers) .
You also need at least one person with a senior management/financial background who can scrutinise the accounts and ensure that everything is being done properly. (my friend was a governor in a primary where the head did not want governors to see the accounts before the meeting in which they had to be signed off...) Budgets in bigger schools can be several million per year.
It would also be useful to have someone who knows something about buildings and their management.
So this is one of the few things I agree with NM about - you do need these kinds of skills. The problem comes in schools where the parent body doesn't have those skills. Not many people who dont have kids in a school willing to give up the necessary time.
In the good old days the head had backup in the LA - their HR experts, their legal team (I did speak to them once when dealing with a complex complaint by a parent) their finance team, their estates dept (who could advise on buildings - like the night the school concert was interrupted with then news that contractors had discovered a serious structural defect in all the corridors- I thought someone had died when the head and I were called out - and it was the authority's estates manager who'd turned out at 9pm ) and so on.
The LA were up the road and could pop in if needed. An academy sponsor may have some of these skills but they may be in an office 6 counties away.