They are not illegal as such, they are not on the CITES listings and are classed "Lower threat". They are native from Oregon coast through the Gulf of California (Baja, Mexico). California has a possession limit of 3 and a minimum size limit of 36", Oregon has a possession limit of 6 and I believe no current size limit, in both places they must be legally taken by hook and line. I have no idea what the Mexican regulations are. In California and Oregon the person who collects one must be in possession of a valid fishing liscense and take the fish legally, it must comply to size limits. To transfer possession legally a form must be obtained from F+WL, filled in and turned in with copies being retained by involved parties.
The people recently busted for leopard sharks illegally caught or obtained undersized fish from California waters (yes, they can tell).
While small leopard sharks in the UK are probably illegally obtained from California waters it is possible (barely) that they are legal fish from Oregon, Mexico, or even captive bred.