I know I'm late to the conversation, but APEX Gun Parts has demilled No1MkIII recv'rs (back half) which have the charger bridge in tact. $20.
Don't know if that'd help or not.

https://www.apexgunparts.com/rifles/bolt-action/lee-enfield/enfield-1-mkiii.html

Scroll down to the lower offerings on page#2 of the No1MkIII parts..

I've done business with them buying parts for No1 rifles to restore in the past and have found them to be good to deal with.