Geezer - still not sure you have set this out clearly.
As I understand it a group can collectively rent an airplane (and share the cost) - the only stipulation is that it has to be public register and flow yy a commercial pilot.
Sounds to me as if that is what you are proposing.
The fact that the group - all of them or some of them may own shares in the airplane is irrelevant.
Best way to get a definitive answer it to have a properly worded question put to the aviation authorities - CLARITY and PRECISION in what you are asking will give you a definitive answer.
Bookworm - cannot be 100% on UK operations but in the US and here in the Caribbean it is very clear.
Commercial reg - so 50 and 100 hr checks in addition to the annual.
No "holding out" that is what makes it a commercial operation; in this case one is not advertising or holding out a service to the general public.
But if a group of friends want to operate a shared airplane no problems - just you must have a commercial pilot or a private pilot must pay his full share of the costs.
I still think this question is not framed correctly.