You dont need to join any scheme to do any electrical work
You do not have to have any qualifications to do electrical work
This applies to domestic/industrial and commercial
If you do any electrical work,you would need to make sure that you were abiding by the H+S legistlation and Electricity at work regs
One way of showing compliance is to work to BS7671 or an equivelant standard
By obtaining the 2391 you have taken an examination that should,(if ever something bad happened and you find yourself in court for breaches of those acts of parliament) be in a position to demonstrate a level of competence that should favour you
You need join no scheme to do PIRs but you may find that without registration with an approved body like the NICEIC ,not much work would come your way,but it is not a requirement
Domestic part p is another where you may or may not join a scheme
There are 2 seperate routes to notifiable work Become self certificating with a scheme or use LABC route and pay them lots of money
Again anyone of any level of competence can carry out electrical installation,it is the procedures that are different for different people and need to be abided by