Isn't the real issue that with geographic locations or hiding them is that ultimately if you are based in Manchester, and would like to work across the country and places like London, is that your business is always going to be listed as in Manchester.
Reason I say this is because people choose photographers in three ways.
1. Recommendations from a friend.
2. Reputation.
3. Yellow Pages or similar.
I would imagine that most people, looking for the likes of wedding photography, photography for an event or business would use the Yellow Pages, unless they had been given a recommendation by someone else.
Therefore, if I was in need of a Photographer in London right now, I'd look at Yellow Pages and see all the different local listings and then be able to contact them or look at their portfolios online.
However, in your case, as you are Manchester based, I'm never going to see an ad for you as your not local to the area.
See what I mean?