Just looked it up, and it seems we can not bring flowers or plants into the UK without a phytosanitary certificate, which means certificate of plant health. If bringing from the EU it is allowed, no idea why, but a plant from the EU seems to be just as likely to carry disease as one that’s not.
With regard to allergies, I cannot see why plants or flowers are allowed in plane cabins.
They could indeed cause a severe allergic reaction in some people.
Apart from that, I imagine they’d be a nuisance to store and could make people trying to put a case in the cabin cupboard rather annoyed if someone else was asking for their plant to be protected.
So a big no from me for animals and plants in cabins. It’s not as if a plant can’t be easily bought in the country of origin.