Unfortunately this is a completely bogus piece of work. After a few google searches I couldn't find any evidence of a 'Sir Edwin Berkhart' or any trace of the original study, although this article seems to have been reproduced a lot.
Also, looking at the author of the column, it says Mark C. Miller, Humorist.
http://m.huffpost.com/us/author/mark-writer-841Don't get me wrong, I wanted this to be legit, but my warning bells started going off when I saw the word "proving" - real science very rarely uses this.
That and: "The fewer clothes women wear, the more their bodies are exposed to nature’s elements, which are life-enhancing." just seemed like a broadly unscientific statement as well. Skin cancer occurs 'naturally' after all
Sorry everyone