Pamela Willis, Curator at the Museum of the Order of St John, explained why the logo was on police boxes in the first place:
'The police were all trained in first aid by the St John Ambulance Association, and police boxes all had the Association badge on them to show that trained help and first aid equipment was available.’
This sign is about 6 in. across and is in 2 colors. This would make any Doctor Who fan happy. (Other that they took the sign off for the New Doctor Jodi Whitaker)
The St. Johns Amblunce Assoctition Sign used in the 1960's with William Hartnell and the movie with Peter Cushing can be found here. https://www.ebay.com/itm/162747805126