It's hard to say. You'd have to get the tape measure out. As long as the centre 75% width of the tyre has at least 1.6mm of tread on it, then its legal.
Fully explained here:
http://www.etyres.co.uk/uk-tyre-law
My interpretation of that would be, that the worn edge that you have is legally allowed to have no tread.... EDIT:As long as the centre treaded section is 75% of the total width.
Most tyres have a legal limit indicator built in, but it's hard to see unless you are looking for it. It's a rubber ridge that runs across the tyre (widthways) and is exactly 1.6mm. There's about 4 of them on each tyre.