My philosophy is it's better safe than sorry. It's much easier to just being forthcoming and not have to worry about withholding any information, saying the right things, etc. Not only is it easier, but more importantly, we're legally obligated to give truthful responses.
My fiance is in the same situation. Struggled with depression during a bad time in his life, was diagnosed by a GP, but never pursued medication/etc, has never self-harmed, does not want to harm others, etc. He's requested a letter from his GP stating he's not a threat to himself or others and it has all been a very easy process, I think it cost him 30 pounds.