Pretty sure this is absolutely
nothing to do with the P and other marks on your apothecary piece however , interesting nonetheless

.. in a court case from 1838, it seems that Apsley Pellatt had a 'private mould' for making square bottles (referred to as 'narrow mouth squares'). They were made for a customer by mistake and they have a 'small P' on them according to the court case (they were stolen from Pellatt's I think, so the person in question was in court with Pellatt).
https://www.oldbaileyonline.org/record/t18380226Can't link directly to the case note so you have to 'control find' and type Pellatt for it to come up.