Here are a few recommendations based on my experience driving out from London ...
First, a few to stay away from: Babington was indeed over run by kids when we were there and the staff was very pretentious (a common theme!). Other than that, the rooms and facilities were excellent.
Barnsley House in the Cotswolds is also a very nice property, but the staff were again very pretentious (and frankly they are WAY over-priced). Also avoid the Hand-Picked Hotel properties as they tend to have nice websites but bedrooms that look like the Hilton.
If you want classic Old English roaring fireplaces and creaky floors, the best we've found is
Gravetye Manor in West Sussex / Surrey (south of London). It's an R&C property. It won't be as modern as Babington, but you will definitely find touches of "quaint" luxury. The food is excellent and the service is usually straight-forward, if not a bit stuffy / old English. These are definitely the biggest fireplaces around! There is a beautiful garden and sweeping views of the countryside. I'm not sure what's around there by way of activities though. When we were there, a bunch of old Englishmen were celebrating their daily hunt in the private dining room.
We really enjoyed
Lucknam Park in the Cotswolds. It is extremely comfortable with excellent staff and really great food and facilities. The pool/spa area is amazing and the rooms are exceptionally comfortable. There is nothing more dramatic than taking the turn down their front driveway up to the property. The other plus for Lucknam Park is all the great activities to take advantage of on-site, from the walking to the horseback riding. It's much more modern than Gravetye -- a very different experience.
The "hot" new property that everyone is buzzing about at the moment is south of London in the New Forest. It's called
Limewood. I've never been, but it's next on the list to visit. So far I've heard nothing but good reviews.
Other interesting properties are
Lords of the Manor (in a tiny, quaint little Cotswolds town) and
Calcot Manor (also in the Cotswolds). I stayed at Lords and it was fine -- a great getaway if you want somewhere quiet.