It will probably depend on the severity of your condition - in each case you'll need to speak to the recruiting section of each organisation, for proper advice.
I seriously doubt it but, as Andy says above you must ask the recruitment officer, I have Psoriasis myself and I haven't found a problem with anything! Good luck!
I recruit for the Fire Service, as long as the psoriasis is controllable we don't have any problem at all! Was asked this about a month ago, unfortunately the man in question also wore glasses - which is a problem. Good luck!