I've never notified standalone electrical work, but I have done submissions for other notifiable stuff, and you have to wait until they come back and say "OK" before you start. (Unless you take the Building Notice route, which costs more and increases your risks, a kind of lose-lose situation.)
On the application you have to describe how you will ensure that the proposed work will comply with the applicable Building Regulations, in this case Part P. Once they agree, you have to stick to that way - there are tales of woe here from people who have done something different to what their LABC agreed to and who found that they could not get their completion certificate.
