Paul,
1085 runs on 430/1160-15 front and 530/1500-15 rear Dunlop CR82 race tyres and you will be able to order them and have them shipped to you.
Please realise though that these are racing tyres and not strictly road legal. They will never work properly until brought up to temperature and will "go off" after so many heat cycles. They are a historic pattern tyre and thin walled and will not take kindly to road use and verge or kerb clipping, so please be warned.
They look great, but in my opinion, should not be used for "general" road use. Dunlop do not mark them "for racing only" which helps a little, but they are not fully "e marked", which could lead to problems with testers, police or insurance claims.
Hope this helps you,
Graham.