I think British beef tastes fine, but if you disagree maybe it's because it's not been stuffed full of genetically modified grain? In the UK, cattle are primarily forage-fed - allowed to roam in pastures (such as the Yorkshire Dales) and eat grass. In the US, beef is grain-fed and generally kept confined in a pen or barn.
We buy most of our beef from our local butcher, who sources it from right here in the Yorkshire Dales. I'll just make my burgers by hand from his ground mince, but I've also had great burgers at places like our local - so I think it just depends on the restaurant really.
Also, if you're buying beef at one of the major supermarkets - make sure you read your labels carefully, or you might not be buying British beef at all - it might have been imported from Argentina.