As I understand it a "Skilled" person can undertake work provided it is then checked and Part P certified by a qualified electrician.
Then you understand wrongly.
The system doesn't allow for <random person> to do the work, and then <random qualified person> to "sign it off". When it's notified through a scheme, that person doing the notifying is making a statement that
he (or she) has designed, installed, and tested the installation to whatever standards. If some random other person has done the work, then that statement is false. Not to say it doesn't happen
Speaking personally, I too would find it very useful if there were scope in the system to legitimately do work and then have a qualified person inspect and "sign it off".
There is a mechanism to deal with teams of electricians - in this case I assume the employer is the scheme member, and the individual electricians will be working under the responsible person's instruction and oversight. In the same way, an individual electrician can employ others to assist with any installation - but he still has to sign it off as his own work.
If someone is prepared to work with you assisting, and then sign it off, then that will work - of course, how much he does and how much the assistant does is down to the judgement of the person who has to put his name to it. This is your best way of doing the work legally - work with the person who is going to have to put his name to it, and you can do as much of the work as he is prepared to let you.