Thank you once again for an in depth answer.There are lots of issues around being a business, even down to choosing to be a sole trader, or a Ltd company, etc. They all have advantages and disadvantages, and really some of the decisions will need advice from a professional accountant, etc, depending on your circumstances and plans.
Make sure you have a separate account for your business. You are supposed to open a business account for this, and if Ltd company then no other options but all you get from a "business account" is lots of charges that you don't get on a personal account! So if doing small stuff first then at least open a separate account for work and remember that is for work, it is not your money, it is your business' money. You, as "your business", can decide to pay yourself money and obviously you need to, but keep them separate for accounting visibility or you will get in to all sorts of trouble down the line.
Accountants will advise you get familiar with some packages like Xero, Quickbooks, etc as they will save you time and money in the long term and HMRC now insist on digital tax returns for most people. We use Xero as our accountant recommended that and provides support for it, but whoever you have for advice might have one that suits you better.
As above, get insurance for your work. It can save your bacon if something goes wrong and letting folks know you have it is the mark of a professional.
If doing small stuff you probably don't need trade accounts at multiple wholesale outlets but having at least one with someone local who gives you decent prices (i.e. not CEF!) is very desirable. But you probably will find the likes of Screwfix are good for T&E cable, etc.
Same with scheme membership. For jobs falling under Part P it makes sense to pay the £500-ish per year and jump through the hoops due to the saving of not having to get LABC to certify stuff at extra cost as you would save the cost over a handful of such jobs, but for repairs and small jobs not worth bothering at first.
I will have a look at some of the stuff you’ve mentioned