We've stayed at Burford a couple of times and found it a lovely place - usual CC high standards. Beautiful area, many lovely villages, and Burford itself is well worth visiting. Of course the Cotswold Wild Life is just across the road, and is excellent. Very good cycling country
Haven't stayed at Cirencester Park (only 30 minutes from home), but it always gets glowing reports. There's an article about it in the latest En Route. No cycling allowed in the park. Cirencester is beautiful, and you can walk right in from the site.
Graham