thanks for your sleuthing Anne. The R/Brierley backstamp I see quite commonly is that shown in the first pic. (a hand written looking backstamp) - however, this rummer has a backstamp as shown in the second pic. - simply the word Brierley in upper case, and which oddly I'd not seen before - maybe it's used for particular production pieces - this is decorated with copper wheel engraving only, no cutting in the usual sense.
I can't believe that this glass is very old - perphaps no more than 30 - 40 years, certainly the underside of the foot has a quite modern look - am I correct in thinking that Royal Brierley ceased in c. 2000?
Dodsworth (British Glass Between the Wars) comments that during the 1960's, the factory used the word 'Brierley' in various forms - so perhaps this is one of those.