My dear boy, Britain runs on capitalism just like the United States. If your family is wealthy enough, you are whatever class your wealth and lifestyle denotes. In terms of wealth, Mrs. Beckham and Mr. Elba are likely equals. Upper or upper middle class doesn't automatically start handing out peerages and estates. They're just wealthy people.

I believe she was named Posh because of her attitude, but I can't say I was up on gossip rags at the time.