Not a lot, Baz.
BUT.............. it would depend on your builder. A good one has developed a relationship over years with Council chaps. I've seen several come and go over time. I've have never fallen out with any of them, and I'm nothing special.
Having said that, I also know some who used to be Local Authority, but went private.
I don't suppose you've got your builder fixed up yet. It might be a good idea to sound out the builders you are going to invite to tender.
Believe me, the last thing you want is to be caught in the middle between the builder and the inspector in any dispute.
As far as you're concerned, the prices are good and fair.
If no one has any preference (or prejudice) then you'll be Ok.
I haven't seen JackTheHat around today. She should have some opinion on this.