I think you're mistaken, but I'm happy to be pointed at a URL.

After investigating further, I've found it is in Approved Document G3. It
does seem more strictly defined than other such "competent person"
situations, but I think there is still a loophole. I am not a lawyer,
though, so if intending to do this, you should check with your local
building control before doing anything to ensure that they agree.

"3.8 The unit or package should be installed by a competent person i.e. one
holding a current Registered Operative identity card..."

It goes on to list various bodies. Although this indeed might suggest that
it is not permitted, I doubt that legally speaking the use of "i.e." could
be said to exclude other competent people. (Again, I'm not a lawyer, so
maybe it can so exclude alternatives). One thing is not in doubt though. You
certainly need to be in one of those bodies to be able to self certificate
the work. You would, therefore, need to get approval from the building
control department, which could be costly and involve an inspection.

Christian.

P.S. It is 15 litres for the exemption, not 13 litres.