Hello Lewis, welcome to the forum. I will try to give a bit more meat on the bones of how & what Part P is to complement what the others have already said.
Part-P is one of a number of building regulations that has relevance when undertaking domestic electrical installations and alterations, it specifically relates to Electrical Safety in Dwellings;
https://www.gov.uk/government/publications/electrical-safety-approved-document-p But there are numerous other building regulations that also have relevance and should be adhered to when undertaking electrical work, e.g. Part A Structure, Part M access & use of buildings, Part F ventilation, etc;
https://www.gov.uk/government/collections/approved-documents Yet for some reason you don't see anyone advertising Part F courses or Part M courses! Any person with a good grasp of English and an internet connection can download any or all of the approved documents to gain a full understanding of what they are without needing a course!
However the traditional historically recognised electrical qualifications are the various City & Guilds courses, (numbers & titles have changed over the years), which cover the theory & science of electrical theory. Practical design & installation. Understanding the current edition of wiring regulations, Inspection &Testing etc. These are the sort of courses you need if you want to become an electrician. The "part-P" bandwagon came about around 2005-2006 when the new statutory building regulations were introduced. These required certain electrical work to have a Building regulations compliance certificate to be issued as well as the BS761 electrical certificate(s). A qualified electrician doing any notifiable work either had to pay a fee, and arrange with the local council building control, to come out and inspect the work to verify compliance with Part P. Or they could become a member of the various trade bodies that Evans mentioned, so they could sign off and notify their own work.
When Part P was introduced many existing electricians who were doing domestic notifiable work, needed to bring some of their qualifications up-to-date, e.g. formal qualification relating to the current wiring regulations. (They did not need to do all the basics of theory & science and installation again, just a current regs update). This was where the Part-P packages started to emerge, quick update for existing electricians to bring them back up to speed with current regs. they were never intended as a comprehensive course for a novice to start from scratch. Yet for some obscure reason the phrase Part-P has become a name many think refers to a full traditional electrical qualification. It isn't and it Never was. An easy tell-tail sign is if a course advertised as Part-P also includes "Portable Appliance Testing" (PAT), as this has No relevance to domestic electrical work anymore than a 'quilting and needlework' course has relevance to someone wanting to become a hairdresser.
I don't think there is even a formal standard or definition of what a "Part-P" course should or should not included? There may actually be some out there that are reasonable in relation to what you are paying. But there is without a doubt far to many that are just a rip-off, taking money from vulnerable people who want to learn a new trade, with absolutely no hope of moving forward after they complete the course. Tread carefully, don't go paying over any money until you are 100% sure you understand what you are getting. As Andy said, the best solution is if you have a local college that offers electrical courses, go and speak to them about what you are aiming for. You may need to book an appointment to go and have a meeting with the head of the electrical department to discuss what courses they offer and what's best for you, But if possible speaking face to face with someone knowledgeable about the range of C&G electrical courses is worth a lot.
Doc H