American English and British English right after colonization were basically the same, with many dialects from Britain transplanted into the US based on their place of origin back in the Old World. Eventually these dialects started diverging in both locations, just due to the distance and the inability to communicate easily with English speakers from Britain.

Regions that had more contact with London and other non-rhotic hubs around London tended to be non-rhotic themselves. These regions were often more homogeneous when it came to their origins for the UK. Some of these dialect regions include portions of Virginia, and large chunks of New England, which still has these features today, though they are losing ground in the young.

The more heterogeneous regions at the time were in Appalachia. Large portions were Scots-Irish, however, and this was a rhotic region in Britain, so it transferred over, and speakers of other dialects in this region slowly developed a rhotic dialect as well.

These were all events largely preceding the revolutionary war, so dialects were shifting, but they would have been more close than they are today. And parts of British were undergoing a lot of change during that time. I don't know the precise time a lot of it changed, but I know Britain diverged first. Usually colonial areas will retain more archaic features of a language longer.

So did George Washington have a British accent, or, rephrased, was his accent any different than that of someone from Britain at that time? Likely, he had an American accent, but it would not have been as significantly different as someone's English in Britain, as it would be today.

Going off of Albion's Seed, which is about the development of regional American cultures out of transplanted regional British cultures, at least some Virginians and other Southerners would have been non-rhotic from very early on (there's a quote in the book of a northern woman admiring a Southern man's arhotic accent).

The Virginian (and I believe other lowland Southern accents) were derived largely from rural southern England, which is where most of the early immigrants to Virginia came from. The most definitive wave of settlement was in the 1640s or 50s, I believe, give or take a decade. By the 1740s (when Washington was growing up), we'd expect some degree of divergence, but Virginian English would probably still be really similar to the English dialects that it spawned from.

We should note that probably all accents at the time would sound very noticeably different from their modern day descendants. So yes, Sam Adams and other Bostonian founding fathers probably had a Boston accent, but they wouldn't sound like Ray Donovan's family. And Tom Paine would have spoken with an (emphasis on "an") English accent, because he was born and raised in England, but it wouldn't sound like any modern day English accent.

Now, one interesting thing to consider is that people often modulate their speech to match prestige dialects, or at least reduce obvious stigmatized regionalisms that could get them made fun of. Given the prestige of England and especially London within the British empire, it's very possible that some founding fathers born in America spoke with an English accent, the same way many Scottish people try to speak RP.