There is no such thing as a Part P qualification, it is simply part of the building regulations, in the early years my son paid for LABC inspection in Liverpool and Chester with no real problem.
However when it came to my parents house in Flintshire, it was very different, Wales up to £2000 worth of work fixed price £100 plus vat, unless exempt, we were exempt as for my mothers disability, however the inspector wanted us to use an independent inspector from his list, even when both my son and I had C&G 2391 etc.
My son said OK but the inspector clearly needs to be higher qualified than us, my dad has a degree in electrical and electronic engineering, only then after seeing we had all the test gear did he allow us to do our own inspection and testing.
So the problem is in the main the fee, £100 plus vat is nothing with a £2000 job, but clearly with a £50 job it presents a problem, in England I think down to each council to set charges, but in Wales still £100 plus vat minimum charge.
Some work does not require registering, however my son found jobs tend to escalate, the want three new sockets in living room, then goes to oh and another two in the kitchen, have you ever tried to explain why fitting sockets in the kitchen costs so much more than living room? OK in England kitchen no longer a special location, but still is in Wales.
Work in places like Llanymynech can really be a problem with one half of a Pub in Wales and other half in England, now no longer a Pub, but so easy not to realise one has crossed the boarder.
But where you live does make a difference, my son found Liverpool council were very helpful, but they can insist on going by the book, getting DNO to disconnect and re-connect for CU change, and not turning on until their inspector has visited, and this changes so much, only some one living in same area can give you an answer.