Voluntary work and mask wearing

[Dollymixture]

My husband wants to do some voluntary work as a van driver redistributing food to hostels and the homeless. He applied and was interviewed and offered a start date.
Now the issue is they are insisting that he must wear a mask unless exempt.
He is exempt due to autism and sensory issues.
They have asked for medical proof of this sitting he is exempt.

Contacted GP who said no one needs to show proof of being exempt anymore as it’s not law now and to download something off gov website to show company.

Company said no, not enough, need proof and have requested he gives them written permission to access to his medical records directly!

GP said even if he does that, they will not be giving him an access to medical details.

So my question is - can the company actually insist on medical proof of exemption even with the change of rules regarding mask wearing? And how do we get it if the Gp insists they won’t do it as it is not necessary anymore.