Wee one
“Entering other than the fwd cg (5%) requires an approved procedure”
The procedure is in the FCOM 11.40.26, it says “Displays default or manually entered cruise CG. Entry of actual cruise CG may increase maximum altitude.”
“youll find a max alt much higher”
It is only about 2-300ft higher in practice, not really "much higher".
“The UKcaa does not allow my company to do it”
The UK CAA allows many airlines to do it. Maybe your procedure was not to their liking? If the CAA really did not like it, they would have had Boeing remove the field.
The cruise CG is similar in value to the take-off CG that you will find on a loadsheet. One often used correction is to subtract 4 (figure will vary with series of a/c) from the MACTOW figure as that is the maximum possible CG shift due to fuel burn. On 1-500 series, cruise CG could be read directly off the trim wheel. I see no problem in entering the cruise CG into the FMC.
FYI the Boeing default, and FFA rules, CRZ CG is anywhere between 18 and 22%. The physics are no different on that side of the pond
