It is not illegal for you to own/borrow the RIF so should be no worries there.
Ideally the RIF should be in the boot and preferably either in the original box or a gun bag/holdall.
If you are stopped for some reason and the police decide to check out your boot then it would help if you have a site membership on you - just helps show what you are doing. If you have the phone number for the site you could offer the police the use of your mobile phone so that they can call the site tpo check that you are booked in that day.
What will happen? That may depend on the particular police officer who stops you and what mood they are in (I know it shouldn't but they are only human and can be having a bad day).
In most cases they would accept that you are genuine and wish you a good day. Worst case, I suppose they could take you to the station to help further and just generally mess you about. If they tried to say you were carrying the RIF in public they might be able to hold onto your gun for a while but all the paperwork would have to go to the department that decides if a prosecution will hold up and I doubt they would want to try their luck as any half good solicitor should be able to rip the case apart.
They could do a bit of a check around your car - road tax, tyre wear, lights etc.
The last time I got pulled over was about 8 years ago when I had one brake light not working but it is a long time since I was 17 so maybe the chances of you being stopped and greater than mine.
Bottom line - drive safely, keep the gun covered and don't worry about it.
P.S. this is only my opinion and does not constitute legal advise. If you get puulled over by an armed response unit who use you for target practice then I accept no responsibility
