Your correct in that the tuner on your TV will not be able to tune either off air transmissions or (more commonly in the USA) cable.
Your TV is capable of receiving a NTSC signal on the scart so you have two options.
1) Use a US VCR as the tuner (you can get these in WAL-MART for as little as $50) and connect to the scart.
2) Use a Satellite receiver - either DIRECT TV or DISH Network (my favourite). I think this is the best option for picture quality. You can connect via S video. Dish network sell a combned PVR/receiver for about $200. You will also be able to get BBC AMERICA on this system (I think its also on Direct TV these days).
I have used both 1 and 2 while I lived in the USA. Off course you'll need a transformer. I bought mine at
http://www.action-electronics.com/trnsupdn.htm
One piece of advice - buy a SCART to S video/phono plug in the UK before you go. SCART is not in use in the USA.