Are there any UK public based databases available on the internet
which you can use to locate a person's (who lives in London) e=mail
address .  I only have the person's first name (which is unusual) and
the surname begins with a "B"

Try this beta email search at:

http://www.iaf.net/frames/email.htm

It's not specific to the UK, but it does allow a search on just the
first name, and it will show some location information if it's
available.