Hi Ste and welcome to PHO from me
I am ex-Army and saw 12 years service. During my last year of service I was diagnosed with psoriasis although it was'nt the reason I left the Army. Numerous colleagues though who had medical issues were drummed out, no questions asked !!
When you apply for selection to join the Forces you will undergo a very strict medical examination and their findings will determine whether or not you are recruited. It is as 'black and white' as that. There are no grey area's where previous medical conditions are concerned.
As Buster has pointed out, your Army recruitment centre will be able to give you more information. And as SJ has pointed out there is a protocol regarding psoriasis but you will be dealt with very fairly by the recruitment team. Remember they only pick the best ~ harsh, but a fact.