Your mention of a paid job sent up warning signals. Have you looked into the matter of getting a visa to live in the UK for 12 months? You will need to have a visa if you're planning on staying for more than 90 days - and you may need one in order to rent a flat. It can be very difficult to get a visa if you're planning on working while you're there. (Generally, they want you to have the job lined up before you arrive.)

For American expat groups, contact the US Embassy in London website - haven't checked recently, but they usually include a list of expat groups buried somewhere on the site. There are quite a few groups in and around London - which might indicate you should look for towns along the main transit lines to make access easier.

Council tax is one of those inescapable nuisances of life - and I guess in the UK these days they are levying it on the occupants rather than the building owners. (When I lived there, they were changing from one system to another and I can't remember what it was we paid and to whom.)
Cheers,
Bev