How about 'Visit our Worldwide Web Site on the information superhighway using hypertext protocol by typing the following characters into your personal computer:' as the standard prefix?
I think Iceland foods lorries still have Iceland.co.uk on the side. Always looked like a web address to me, but never went there until 5 minutes ago.
If it is for display use (i.e. anything that a person rather than a computer will read) then it needn't have the www. or any other prefix. If people can't realise that it is a web address they will probably have bigger problems with using a website.
The less meaningless (to people) code/protocol junk the better.
If it was needed to be clearer, I'd add to the text http://edge... rather then www.edge...
Also, while people who don't look at .ac.uk sites might find it a little less obvious, I would expect this metric to be improved by the fact most people looking at the link will be exposed to many .ac.uk links, so more used to that been a web domain then the "general public".