TMZ is claiming that "British Britney" is just one of many personalities Britney Spears has (The weepy girl, the diva, the incoherent girl are a few of the others). In medical terms. Britney [probably] has "Dissociative Identity Disorder" (DID). The American Psychiatric Association defines the disease as:

"A mental illness in which a single person displays multiple distinct identities or personalities, each with its own pattern of perceiving and interacting with the environment. The diagnosis requires that at least two personalities routinely take control of the individual's behavior with an associated memory loss that goes beyond normal forgetfulness, and symptoms are not due to substance abuse or medical condition."

That memory loss aspect of DID fits in with what sources told TMZ:

We're told when Spears loses the British personality, she has absolutely no idea what she did during the time she assumed that personality. Sources say Britney had become the British girl the day she didn't show for her deposition and has no recollection of it. (Source)

Well this explains her propensity to order multiple combo meals whenever she goes to McDonalds, "Regular Britney wants a nummer four and . . . just a sec, whadduya want British Britney . . . ya'll got any fish an chips? OK some of that. Shameful Overeater Britney wants some bacon, a tube of cookie dough, and a dark corner, ya'll got that?"