"In a
small number of cases, particularly among asthma sufferers,
there can be the risk of a severe asthma attack, and there
have been very occasional reports of the most severe, lifethreatening
form of allergy (anaphylaxis). "
"You may also be advised to use a preventer (steroid) inhaler and nasal spray
starting the day before any unavoidable exposure, for example a planned visit to a home where you know there
is a cat.
As stated above, if your doctor believes your symptoms could be very severe, you are likely to be prescribed
adrenaline (also known as epinephrine) The adrenaline injectors prescribed in the UK at present are
Emerade®, EpiPen® and Jext®."
Anyway, unless you're constantly carrying around dogs or have unusually severe allergies, this seems like a minor irritant.