To Dean and other fine Britons, you may not realize this, but the general English/Welsh accent around the time of the American Revolution was more... well... American.
Basically, you know how the American accent stresses the 'r' sounds? How 'centuh' becomes 'centerr'? Well, your great-great-grandparents (if your family has been Anglo-Saxon from at least then) probably sounded more like the Yanks instead of sounding like the Standard BBC English accent. Non-rhotic accents (the one which doesn't curl the tongue as much and thus leaves out the hard 'r') did indeed exist at the time, but they were only spoken by the upper class, notable around Cambridge.
In the 1800s, due to education reforms in the Victorian era, the non-rhotic accent became standardised and here you are sounding like that!
Much of the spelling and written language is exactly the same as the late 1700s, it's just that instead of the American accent jumping off from the main English 'accent tree', the one spoken by British commoners would be a mix between rhotic and non-rhotic accents. Want an example? Listen to the Boston, Brooklyn and Charleston accents. That would have been what the everyday Londoner would have sounded like circa 1775.
Spelling and word differences are largely American though, mostly taken from Dutch, Norwegian Gaelic (Irish) and Native American languages.
Don't know why you guys drive on the left. When we invented the automobile. Made to drive on the right.