I think they call him "Chef Ramsey" to inform the uninitiated as to why this rude and disagreeable man is on TV at all.

It is interesting that the US media does and did not use the same standard for Jamie Oliver, Julia Child, Graham Kerr, Yan of "Wok with Yan" or Emeril; all of whom, in my opinion, are more deserving of the title.

Likewise, in saying "Prime Minister Cameron", they may be simply informing those who don't closely follow UK politics, just about everyone, which "Cameron" they were talking about; thus preempting thoughts like "Who cares what Kirk Cameron has to say about the banking crisis."

On the other hand there are a lot of protocols referring to how the Office of President is to be respected so it is rightly "President" or "Mr." Obama here, just as all of his predecessors were respected.
No one expects the UK Press to follow such rules on internal reporting, but if my memory serves me correctly, BBC broadcasts meant for an audience which includes the USA do use these honourifics.