It's also alleged it began in Castleford, where he once perfomed at a local theatre/club (in 50's/early 60s)
The girls who were the dancers (& possibly barmaids) used a dressing room, that opened onto a public area, so hence the phrase, to stop the punters seeing them undressed
Plus, it's also supposed to be Grayson, on what is (officially) Centurian House, the local job centre at the bottom of Bank Street, near junction with Aire Street
https://www.geograph.org.uk/photo/2016748
View attachment 556877
Why 'Centurion'?
Castleford was a Roman settlement/fort, where the River Aire was forded (to them it was
Lagentivm)