I think it might mean P for pauper or poor.There was a tax introduced around then for entries made in the records. The P would signify that they were poor and were not charged a fee. Gadget
Generally, I have noticed a high incidence of 'P' descriptions attached to baptisms and burials in the registers of some parishes. Other registers are unusually lacking in what one would consider to be a reflection of an average occurrence of poor within a parish. Without having examined the Overseer's Accounts of every parish where anomalies have been found, I can only think that perhaps the high incident rate of baptisms and burials exempt from the tax were performed by overtly sympathetic clerics. It seems that many clerics were highly sensitive and empathetic to the stringent economic realities endured by the members of their congregation and did what they could, within the confines of secular and ecclesiastical law, to relieve the expense of unpopular taxes.