A very interesting topic.

Theresa May's British accent poses no problems for Americans.  No surprise here, as she, as well as most of the upper crust of the English society, the Queen, the royals and the BBC included, of course, use what is called RP (Received Pronunciation).  Discussions on the internet note that the actual character of RP developed as a partly conscious and partly unconscious attempt by upper-class speakers to distinguish themselves from those of the ‘lower orders’.  On account of this, it is perhaps less than accurate to call Theresa May's the British pronunciation.  It's also worth noting that "attitudes to RP have changed. For most of the 20th century it was the uncontested prestige accent of Britain. It was valued for its associations with the World War years, the Royal Family, and classical actors such as Laurence Olivier. But in the closing decades a fundamental change took place, reflecting a society in which successive waves of immigration, greater work opportunities for regional speakers, and the rapid increase in local commercial radio introduced an unprecedented array of new voices and listening experiences."