British pronunciation

I have just finished an article in the September 13, 2012, issue of the London Review of Books. It concerns a courageous British diplomat in the early 20th century. It contains this sentence:

“[A professor] asked … if it was true that ‘ck’ in the name ‘Cockburn’ was not pronounced.”

The answer is never given in the article. May I ask someone to give me the answer?

Thank you.

Fashionable speech suggests that you pronounce this without the ‘ck’ sounded.

Thank you, Alan.