My late father was an inspector in the Post Office in Liverpool involved in the mechanised sorting of mail and often showed groups around the head post office sorting office.
If you are a member of a club or other organisation then you could try applying to your local sorting office.
Obviously the larger the town or city will have a much more mechanised installation with sorting machines etc. demonstrating how the use of post codes and phosphor banded postage stamps have transformed the sorting of mail since the early 1960's. smaller local sorting offices will tend to be more manually based.
They will only allow groups of people from a recognised club etc. you as an individual would not get a look in.
Good luck, I hope you succeed.