No medical advice....you already know that cold, dry air and the stress you mentioned can cause an asthmatic to trap air on ascent...the question as a diver, and only you can answer it, is are you willing to assume that risk? We hear call level of risk a "roll of the dice"; if it comes up snake eyes, you lose everything. Strictly as a fellow diver remember if you embolize your fellow divers will also pay a price.
Diving is always about assumption of risk...good luck and I am sure you can find a diving medicine doctor in UK.
PS...Our Dive Manual and Standards list asthma as an "absolute contraindication" for diving. Asthma by definition is 'air trapping' and the degree of air trapping may be a moot point; like being a 'little bit pregnant' overexpansion forcing an AGE is the risk. It only takes one.