Suibhne.

African Head Charge...... there's a blast from the past, I have a couple of their albums gracing my CD shelf (along with lots of other from the On-U-Sound "family").

I agree they have lots of "trad" elements in their music, but it's not British Trad (whatever that is!) which is what I think the OP was asking about.

There's an album by Little Axe, AKA Skip McDonald (also associated with On-U-Sound) which is blues and reggae based which is interesting. Can't remember the name of it just now but I can wander downstairs and look if anyone is interested.