“Since the LA gets its pupil premium for SB whether she goes to school or not, i would have thought it should have to provide an examination centre.”

I didn’t know this. My understanding is that the LA doesn’t get funding for pupils not registered at a state school as of some date or projected value long ago, then the amount each school received is based on the school census date some time in January. Funding is complicated but I didn’t know Home Ed and presumably privately educated children are counted in assessing funding.

Also the pupil premium is a separate thing entirely for those on free school meals or “looked after” children or maybe some other factors too (statemented?). It’s an additional amount.

Some areas do allow the home educated children to sit at pupil referral centres but I wouldn’t take that even free as have heard some intimidation from the students to the home educated ones (they may not have been deliberately intending to intimidate but the home ed child felt intimidated)

I think I had more to comment but I’ve forgotten so will re read and come back.