Second Limewood, really lovely albeit quite a busy place. The Newt in Somerset is incredible value for money if you manage to get a room. Beautiful hotel with a spa that is not massive but is gorgeous and the ladies who give treatments are fabulous.
I have reviewed it on my blog and I also listed other hotels with spa not far from London (Chewton Glen, Coworth Park, Soho Farmhouse etc) on my blog, if that's useful:
https://fromthepoolside.com/advanced-search/?_sft_category=uk&_sft_accommodation=hotels&_sft_post_tag=spa
For stylish family holiday ideas in hotels and villas with pools, visit https://fromthepoolside.com