In the Rough Ride Guide Book there’s a 27 mile route starting from Mere that effectively heads west through woodland. It does state that King’s Wood is part of Stour Estate and you’d need to phone for permission, should be free for a one off. It continues through more woodland eventually coming out at Horningsham where you’ll reach open country.
It heads S from Horningsham where you’ll reach a dizzy height of 273 metres. Heads towards Kingston Deverill then picks up a track alongside a gliding club heading W.
Let me know if you want details instructions or a gpx.
I would highly recommend the Wylye Valley area that is effectively E from Mere. Again, fantastic views from very quiet tracks.
Edit: Just checked Ian White’s book and his route encompasses considerably more open country. Which route of his did you not like then? I’ve followed a few of his and have been happy.
Further edit: The cover pic is taken in the Wylye Valley, at the bottom of Stockton Down.