We would like a recommendation for a short-term (e.g. one week) apartment rental service in London or alternatively an inexpensive hotel.

I would NOT recommend the Citadines Trafalgar. We stayed there for 3 days/2 nights last summer, $900+.

You cannot beat the location, and the staff was ok. However, the AC quit working and when I asked the desk about it the answer was "well, it is a problem all over the hotel, sorry".

Since the windows didn't really open then it got pretty hot and stuffy in there. And the cost was way above what you got for your money.

Travelodge Covent garden
Citadines Holborn

both are central and are usually reasonably priced

Hello try www.waytostay.com for London rentals, although im not sure what you mean by inexpensive exactly.
Was in London 2 weeks ago, the Euro-sterling exchange rate is great!
I recommend the London bridge area and around Vauxhall-Kennington.

Hadn't been to Soho in years and i forgot how charming it is.

Those are essentially hotels. for apartments, see this thread:

http://www.fodors.com/forums/threadselect.jsp?fid=2

• What is your budget?
• How many of you?
• When is the trip?

All of this info is really essential before we can give much useful advice.