You don't really have to use the dreaded M4, thus avoiding the "entry fee". If you head a bit further north you can turn left and enter the Land of Dragons through Usk and Monmouth. From there, the world as they say is your oyster.
Croeso (that's "welcome" to the un-educated).
Thats the way i would go as I'm midlands based, but i thought being from somerset it might be quicker across the bridge.