@WiltingWallfower - without wanting to out you, you're not in Gloucestershire are you?!
I have two SEN DC and like you, could fill a book on the failings of that division. As could many of the local SEN parents I know.
The Planning department was a fiasco. Applied in April and didn't get approved until October - missed all of their own deadlines by months. They'd restructured the department and the issue was that there was only one person who was allowed to sign off the decisions formally - and they were barely in the office.
We only got a decision in October as I rang up begging and pleading because my DM is disabled and we desperately needed the work done before winter. Similar to you, neighbours happy with the plans, no objections - a very simple design. It was only the lack of a signature that held it up. I feel sorry for the poor people working in that department.
However, building control - different kettle of fish entirely. We used the LA BC, not private and I have to say they have been brilliant. Really great at providing advice on the phone, couldn't be more helpful with random questions. We've used two different building firms for different elements of the project and both are very happy with BC from our LA.
Also worth mentioning that if you're disabled, some types of work are exempt from building control fees from the LA.