'I wonder how Henry VIII and Elizabeth I spoke. It's a pity we don't have recordings from that time!'
Ben Crystal has done some excellent work on 'Original Pronunciation', and in one video he enacts how Elizabeth I may have sounded if she spoke with OP. It is highly likely that Shakespeare's plays were performed in the accent represented as OP, especially since RP did not exist at that time.
There is also an interesting site on Accent Bias (which is called 'Accent Bias', I believe) which describes some of the 'newer' accents in the UK. One of these newer accents is General Northern English, which is, perhaps, the northern equivalent of RP.
The Great Vowel Shift, which took place between the ages of Chaucer and Shakespeare, influenced some accents. Most famously it resulted in the trap/bath and foot/strut split that became one of the ways through which some southern English accents may be distinguished from most northern English accents.
There was a time when people would not be accepted in the 'higher echelons' or society or in the older professions without a 'plummy' accent that indicated a public school education and an 'upper middle class' background. However, those days have passed, although accentism still exists and reflects wider prejudices in society.