I live near the signposted diversion route and it's a lot busier that usual at the moment ...
This stretch of the A350 is always busy, but there was a serious jam some two miles long the other morning when I had to venture out there. The Department for Transport's map makes it clear why:
Towards the left of the map, you'll see a V shaped pair of congested roads (orange and red). The leftmost one is the A36, closed at present and the one on the right is the A350 which is taking the extra traffic. The red (worst congested) sections are two sections near Melksham,, and between Chippenham and the M4.