Hi Fred,
Even if there were no roadworks I would still go down the A350 instead of going through Bath. Its much less stressful with a caravan in tow. I'm going there at the end of June too and I intend to go to M4 J17.
Heres an extract from my route planner:
09:12 4.9 Merge onto M5
09:41 34.3 At Exit 15, keep LEFT onto Local road(s) 0.3 mi M4 / M32 / M48 / London / Bristol / S. Wales
09:41 34.6 Bear RIGHT (West) onto Local road(s) 0.3 mi M4 / M32 / London / Bristol
09:41 34.9 Merge onto M4 20.2 mi
10:01 55.1 At near Stanton St Quintin, stay on M4 (East) 0.1 mi
10:02 55.2 At Exit 17, keep LEFT onto Ramp 0.2 mi A350 / A429 / Chippenham / Cirencester
10:02 55.5 At roundabout, take the FOURTH exit onto A350 2.8 mi
10:05 58.2 At roundabout, take the SECOND exit onto A350 [West Cepen Way] 3.8 mi
10:11 62.0 At roundabout, take the SECOND exit onto A350 4.0 mi
10:17 66.0 At roundabout, take the SECOND exit onto A350 [Beanacre Road] 0.6 mi
10:19 66.6 At roundabout, take the SECOND exit onto A350 [Western Way] 1.1 mi
10:22 67.7 At roundabout, take the SECOND exit onto A350 5.7 mi
10:28 73.4 At roundabout, take the FIRST exit onto A350 [Westbury Road] 2.0 mi
10:32 75.4 At roundabout, take the SECOND exit onto A350 [Trowbridge Road] 0.5 mi
10:33 75.9 Turn LEFT (South-East) onto A350 [Haynes Road] 0.2 mi
10:33 76.0 Turn RIGHT (South-West) onto A350 [Warminster Road] 3.2 mi
10:39 79.2 At roundabout, take the SECOND exit onto A36 1.5 mi
10:41 80.7 At roundabout, take the THIRD exit onto A362 0.7 mi
10:42 81.4 Enter roundabout 43 yds
10:42 81.4 Arrive Longleat House