This route is pretty much heritage bingo, an unsung star of the National Cycle Network.
It starts by the striking Dundas Aqueduct of the Kennet & Avon Canal, swinging off towards Radstock and bohemian Frome on a succession of railway paths (the Collier's Way). A memorable passage through the grounds of Longleat (with a stiff climb) leads into Warminster.
After this it's mostly country lanes along the Wylye valley to Salisbury, circling the cathedral close, heading from there to Eastleigh and the south coast. Longleat aside, it's never taxing, and one of the most enjoyable ways to explore the Wiltshire countryside.