Funny thing is, there are thousands of UK accents that are as different from each other as they are from the generic American accent. Granted, there's variety in the US as well, but the concentration is higher in the UK, as we've had towns and villages for thousands of years within 20 miles of each other that had their own unique way of speaking that often only locals can understand without effort.
So yeah, when you say 'British accent' that means basically nothing to anyone in the UK.