In British people^x, British accent^x, Numbers^x

To tell you the truth, I've never heard any foreigner (unless they learned English when they were very young, or had lived in an English speaking country for at least a decade, and had extensive, and personalized accent coaching) ever be able to pull off either an American or British accent....

I'm an actor, I'm going to start learning some accents just so I have them in my bag of tricks. I was going to start with a single British one, then move on to other countries/accents, then just keep learning more. What would be a good general British one to start with? Is there a dialect...