The met office is excellent, it is a free app for your phone and is as good as they get.
Cotswolds route? I often travel from London to the Welsh borders. The A40 is a good road, but best use the M40 out to Junction 5 to get past various towns, then the 'old' A40 towards Oxford.
The A40 west of Oxford is pleasant, but there are roadworks near Witney which can cause long tailbacks. But you will go by The Farmers Dog (Jeremy Clarkson's pub). Never (yet) been in there, but will do one day. If you carry on along the A40, Northleach is pretty, then past Northleach go left on to the A436 to the Seven Springs roundabouts and then on to Cirencester.
Alternatively, from Oxford, take the A44 north, then through Woodstock (Blenheim Palace) up to Chipping Norton, then a couple of miles north of CN take the A436 to Stow in the Wold, then through Stow on to the B4077. There is a steam train station at Toddington with a cafe. And the B4077 is a very nice road.
Or, stay on the A44 and carry on via Moreton in Marsh and Broadway / Fish Hill to Malvern & Worcester etc.
There is so much to see and visit...
If you have been following the Norton unit 650 thread, this video shows some of the roads you could ride once you get into Wales;
https://www.accessnorton.com/NortonCommando/interesting-650-norton-prototype.40675/post-695798 Llyn Brianne is near Llandovery