When we started the project, the architect suggested we use an independent assessor. Have to say, this is one of the best decisions we made.
They were cheaper than LABC (who price on the completion spend but this excludes kitchens, bathroom fittings etc so could be manipulated to be what you need) and are super responsive but also light touch.
There was a paper exercise up-front to supply all the detail drawings and calcs (these came direct from MBC and the structural engineer who designed the basement) and then details on other elements.
Their first major inspection was when the rebar was in, ahead of any concrete pour. Seeing the quality of the work meant they didn't need to come back until the frame was erected. Next visit was after first fix and we'll see them again near the end.
We've been able to negotiate away an external soil vent stack (their suggestion) and use of fireline plasterboard everywhere plus had sensible discussions on fire doors, escapes etc.
I'd say that they have saved me money and been a good checkpoint for some issues.
One golden rule though - whatever the outcome of a phone conversation - always get it in writing!