Summary
Windows. If you don't use a FENSA-registered contractor you must apply to Building Control for approval. This has applied since 2002.
Electrical work. Apart from very simple work wiring changes to certain rooms (not bathrooms or kitchens), if you don't use an approved electrician who can self-certify his work you must apply to Building Control for approval. This has applied since 2004.
Work on oil or gas systems has always required an approved contractor.
Structural work, changes to the waste pipework has always needed a BC application.
Those are the main ones that can catch DIY householders out.