John Miller is Glaswegian and tours irregularly across the UK but has a great CD out (review online later today) and BapKennedy is from Norn Ireland but hardly every leaves the Province these days which is a shame - he should be a star.
Carrie Elkin and Jeff Finlan tour the UK fairly regularly but I've not heard of most of the others either.
As well as No Depression - check out www.maverick-country.com for reviews and UK Tour dates too.
I can think of one that goes without saying. The Initials are TotM...
also for you Europeans, there are some psychedelic spaghetti western friends of ours called Spindrift doing a tour at present. if you hear of such happening nearby they put on a good live show.