If you don't mind a longish train journey, how about Devon or Cornwall?
Penzance is great, with loads to do in that area. We did it years ago by train, with 3 under-fives. There is masses to do in the town itself, including pebbley beach. If you're into walking, you can walk to villages like Newlyn or Mousehouse. There are buses to places like Marazion, where you can visit St Michael's Mount. Get a train to St Ives for sandy beaches.
Or Newquay, again we did this by train one year. Not really my cup of tea as a place, but has loads of good beaches and things to do - swimming pool, zoo etc. Don't know how good buses are for venturing further afield.
Have a look at a rail map to see what resorts are on the train line - off the top of my head, in Devon you have places like Dawlish and Paignton, don't know how easy a journey it is from London.
Or venture 'up north'. You can get to Whitby by train, although it would be a fair journey from London. You can spend a whole week in Whitby and entertain the whole family without leaving the town. Or go on the steam train from Whitby to Pickering or one of the other places on that line.
What sort of cottage are you after? How many bedrooms etc? I might be able to suggest a cottage from one of the places we've been to.