The existing employer may take a dim view (mine wasn't overjoyed) - but the condition which is preventing you being at work may not prevent you from attending an interview.
When you are off sick it doesn't necessarily mean that you are bedbound. You could be off with a broken leg for example.
I daresay the current employer may not be impressed if they were to find out, but I'm not sure that they could do anything about it? (Although I may be wrong.)
I had a broken foot which prevented me from working & I was properly signed off by the medics for a fortnight.
I happened to have a pre-arranged job interview during that time, which a friend drove me to/from. I was able to hobble into the offices and sit through the interview - I couldn't have done my usual job in that way.
I see no reason why you shouldn't attend the interview, ilovemarkb.
You will probably need to tell the prospective new employer that you are on sick leave (and why) - whether you tell your existing employer that you have an interview is a more tricky decision.
I'm not sure that telling your prospective employers that your off sick due to mental health issues (whatever the cause). I don't see any reason to admit to it in any case (it's non of their business). Anyway, the best of luck Ilovemarkb I hope you find more suitable employment.
They can't disclose the details, 237SJ - but they can give a factual account of 'number of sick days' - which then puts questions in the mind of a prospective employer, which it is better to pre-empt by clarifying during the interview (or written application).