Hello, I'm TV Tech1 and I'll be working with you to identify and help you resolve your problem.
Subtitles are built INTO the TV programme, and the TV stations can turn them on and off too.
The fact that you get subtitles on other TV stations makes me believe the problem is more likely to be the programs or the TV station(s), not the TV set itself.
Now, if they are ALL BBC channels...then I'd suspect the network or the TV station/transmitter. But I doubt channel 1 to 5 are all BBC or ITV network channels in your area.