Hi UK_IS200
Depends on mileage - you'll need to get a pretty high mileage one to get a Sport for 15-16k. I bought my S for 16.5k last september - it's a 2000 V-reg and had just 18k miles on when I bought it. I guess you could get an SE with 30-40k miles for that. Try the lexus web-site - they have a uk wide database of used vehicles that you can search by price etc.
The cars come with the remainder of their 3 year warranty and they check them over before they sell them second hand so there are few worries. There are few common problems - there's a thread here somewhere listing them and the dealers are really good at fixing them under warranty. I had a wheel alignment prob and had 4 shocks replaced, plus wheel alignment done, plus car washed, plus 3ltr RX courtesy car - all under warranty. Apart from that just make sure you check over the paintwork for scratches, stone-chips etc.
BTW I'm in Reading too - the dealers there are truly excellent. Which salesman did you talk to? David dealt with my purchase and was very helpful. When I went in again after a few months he said "Hello Chris" - impressive!