Hi Cabinstar,
I used to operate with Flightline some years ago and remember about a colleague with the same problem.
The company provided him long sleeves, don't know if expecially tailored for him (he was the only one I saw with long sleeves, usually short ones are more comfortable on board) but as long as he covered the tattoo, no one had anything against.
Don't know about major UK companies policy, but maybe you could ask about the possibility of having (probably at your own cost) long sleeves, at the end if the design is the same...probably there won't be any "not uniform charge"