Have a look at sections 6.14, 6.15, 5.9 and 5.4 of this: http://www.basc.org.uk/media/ho_guidance.pdf
Looks like they can't lend you a gun if they have reason to believe you're of unsound mind. (I'm not saying you are!!) They obviously haven't had a reason so far. Unless you have to tell them, I'd keep quiet about the rejection and not give them a possible reason now.