None of us like the idea of our pets in cargo. I can promise you that.
BUT, my vet really reassured me. I moved my two cats.
He explained that animals are much happier in the hold. Their crates must have ample room to stand up and turn around. They are anchored down tight. The area they are in is dark and heated so it's cozy and warm. The lull of the engines soothes them and they usually sleep most of the journey.
He went on to say that if they were in the cabin (which isn't possible for any domestic animals into the UK), they would be restricted in space, with the lights going on and off, feet going by continuously, and the big trolleys going up and down the aisles.
Might have been a load of B.S. but it made me feel a lot better. And my cats were big eyed but happy when they arrived.
I used a pet relocation company (Air Animal) but that was back when it was more difficult to bring animals in. They've relaxed the rules quite a bit since then, so easy enough for people to manage their own paperwork.
I've had a few friends move dogs here and back - with no issues. My friend moved her 14 year old dog back recently and he did beautifully.