I have two of these litter boxes and love them, but they are not "self cleaning" like the LitterMaid boxes that actually rake the litter for you when the cat leaves the box. The OmegaPaw littler boxes need to be rolled over on their side and upside down, then you pull the little drawer out and it has all the waste in the drawer. Also, depending on the size of your cat, they may be too small. So, if you have a large cat, be sure to get the one specified for multiple cats.
If you really want a
self cleaning litter box that cleans itself eachtime it senses the cat has used it, go with the LitterMaid.
Dr. Foster and Smith (
http://www.drsfostersmith.com/) can ship to the UK, it looks like. You have to call to get a shipping quote though...