Army website says;
If your tattoo is offensive, obscene or racist it will prevent you from joining the Army. Small tattoos that aren't offensive in any way are not normally a problem, depending where they are on your body and how visible they are. If you have a tattoo, the best thing is to go to your nearest Army Careers Centre and ask them to check if it's okay.
The MoD policy used to be very clear. Tattoos are only to be held in Edinburgh and feature a lot of men in skirts.