My suggestion would be the Viceroy Sugar Beach on St Lucia - truly stunning location in a world heritage site although it's not the pure white sand and turquoise seas that we in the UK imagine the Caribbean to be. The villas/ rooms all have private plunge pools and having stayed at many hotels discussed on this forum I would consider the service to be amongst the best I've had anywhere. There are other dining opportunities nearby such the restaurant at Boucan - Hotel Chocolat - http://www.hotelchocolat.com/uk/restaurants/about .

The Carlisle Bay is also lovely although I haven't stayed. I've visited when friends stayed and had a walk around. Lovely beach.

Both Antigua and St Lucia are interesting islands with other things to see and do other than lie on the beach. And both are easy journeys from the UK.