If you want to be pedantic about it I'll agree with you that NATS didn't operate at Liverpool. Strike out NATS and replace with any of the following terms that suit your fancy.
CAA, Board of Trade, Department of Transport, Ministry of Aviation. I'd guess Board of Trade but I won't bet on it.
I can't confirm what we were at the time because I didn't keep my payslips or licenses. Had a drawer full of the latter because they reprinted them every time we got shunted to a different ministry.
It was IAL who took over from us - definitely not SERCO.
jb