Anton,
Do you want to avoid motorways? If not (and we travel from Shropshire to South Wales often), maybe try this:
A4123 from Wolvo to J2 of the M5
M5 to J8 (M50)
M50 to Ross
A40 past Monmouth
Keep following signs for Newport
At M4 turn right towards Cardiff
M4 all the way to Pont Abraham near Llanelli
A40 to Carmarthen
If M-Ways are a no-no, try:
A41 or A449 from Wolvo to pick up the M54
M54 to Shrewsbury
Left on to A49 south
At island outside Leominster, 2nd exit into town
Mini island 1st exit
Sharp right after 300 yards
Take right hand lane at traffic lights
Turn right
Straight over mini island (with supermarket on LHS)
Take left fork at pub on left
Follow signs for Brecon
Eventually, you'll cross the River Wye near Glasbury and get to to a T-junction. Turn right.
You'll be on the A438 at this point, and travelling through Aberllynfi, Bronllys, Felinfach etc
At the first island on the Brecon Bypass, take the 2nd exit.
Next island, take the first exit (A470).
Follow this road to the junction with the A465.
Turn right on to the 465
Stay on this road past Hirwaun until it becomes DC, and eventually shortly after passing the exit for Neath on your left you'll get to a large island over the M4.
Turn right on to the M4 westbound (Carmarthen should be signposted)
Keep going to the end of the M4, then pick up the A40 to Carmarthen.
Phew.
Funny how routes that you drive so often and become second nature are difficult to describe
Anyhoo. Hope this helps...