Trying to speak in a British accent is not really easy. Along with the accent are mannerisms that go along with the British themselves. There are hundreds of different accents within Britain, so categorizing it as a ‘British’ accent is rather incorrect; wherever you go you will find an unbelievable variety of different pronunciations. The following directions describe ‘Queen’s English’, rarely ever used in modern day Britain, but the foreigners stereotypical view of how the British talk.
STEPS
Understand that all British accents (barring those from the West Country, Liverpool and parts of Scotland) lack a rhotic r; i.e. don’t roll your "r"s and that not all British Accents are the same; a Scottish accent varies greatly from an English accent, but are both British.
Know that some British accents may be that the ‘T’s are not pronounced and that the u in stupid and duty is pronounced with the y sound, not oo as in an American accent; thus it is pronounced stewpid, not stoopid, etc. The standard English accent, the a (for example in father) is pronounced aah, not like a like apple.
Pronounce that T as T, and not an American D. (Duty is pronounced Dyuty or condensed slightly to Jooty; not doody).
Pronounce the suffix -ing with the g, so it sounds like -ing rather than -een. But sometimes it is shortened to in as in lookin.
Applying the two steps above, the words human being are pronounced h-yuman being rather than yooman been.
Sometimes ‘T’s aren’t pronounced at all, especially in words with two ‘T’s grouped together (this is known as the glottal stop, and is common in American English pronunciation).
Sometimes the ‘H’ is not pronounced, in some accents.
Realise that some words require the ee sound to be pronounced as ee, such as in the word been. In an American accent, this is often pronounced bin. In an English Accent, this may be pronounced been, a homophone of bean; or just as "bin", depending on where you go.
Stop using all of your American slang and replace it with British slang. Understand British Terms.
