Thanks a lot for everyone's interesting replies. I had a careful think about all the suggested options, and decided to get a new flatscreen TV. I got it from a local PC World store, and it cost £250. It's a 32" Toshiba. The image quality is perfectly acceptable. The sound is tinny compared to the "meatier" old Sony tube based TV I had, but that is to be expected. I'm not bothered - it sounds clear enough. Generally speaking, I am pleased with it.

I understand that flat screen TVs use less electricity than old tube based TVs, so perhaps I should think about this as a cost saving investment. Also, the old failing TV is so heavy that I didn't really fancy farting about getting it to a repair shop. But I've got to stick it in the car at some point, to take it to the local recycling centre...I'd rather dump it, because if it is faulty and potentially dangerous, I don't want some unsuspecting person plugging it in and it catch fire.