Lou -
I used to live right down the street from the Citadines Barbican. I never went in, but it looked nice from the outside. It will be about a 15-20 minute walk to your office from that location. The Barbican is a weird area. It's right in the City so Mon-Fri it is busy with business people, but Sat and Sun it is dead. The Barbican is really close to Farringdon, which is full of bars and clubs and pubs for the Friday and Saturday night. There is a decent supermarket within walking distance (Safeway). The Barbican Tube stop is on your doorstep.
One tiger is right that there is a lot involved in finding a flat, but it can be done, just make sure your employer is flexible with taking time off during those two weeks to run to the Estate Agents office to sign this or that. I think I had to visit the estate agent about 4 times in one week before I was able to rent the place I am in now.
Good luck