Matt, go see an accountant and explain to him you are setting up on your own. He will give you the options and explain each one. Ie Sole Trader, Limited Company, Partnership etc. He will register you with HM Custom & Excise.
I set up 12 months ago and have not looked back, sometimes it is difficult with cash flow problems and customers not paying up on time but overall I love it. Make sure you have some cash ready to fall back on in the case of no work or people paying up problems. Also I have spent upwards of ÂŁ15,000 getting set up, van, business cards, advertising budget, test equipment, PAT tester, insurances, NAPIT registration, tools (drills, 110v stuff, steps, ladders, roof rack), sign writing, laptop, printer, 17th edition etc etc
As for Part P, I have been a spark for 11 years I did a full apprenticeship with a local company, then 2391, 2400 and recentlly the 17th edition. I am registered with NAPIT under full scope inc Part P and they asked for 17th edition and 2391 inspect & test as well as liability insurance, indemnity insurance, copy of the regs, onsite guide, guidance notes, electricity at work regs oh and test kits, calibration cert, voltage testers blah blah blah. However I have two friends who have recently set up and they have gone with NICEIC as domestic installers, one has no qualifications and has been a labourer since time began and the other is a 16th edition qualified spark with no 2391 and they only have liability insurance (I find this a little worrying and annoying) the test kit they use was broken at the time of assesment and the assesor let them use his !
What I am saying is there are different paths for diferent people, speak to NIC, NAPIT, Business link they will all give you the information you need to make the right decision in setting up your company.
Go for it and good luck !!