In reply to Iain Peters:
I live just a few miles from Ladram Bay, and know the coast pretty well. We have kayaked to the stacks a couple of times from Budleigh Salterton and I've had the chance to inspect them on a few occasions.
Access to the main beach at the holiday park is obviously very easy. There is a couple of stacks in this bay, one of which you can get to straight off the beach at low water. At dead low tide you can get around to most of the other stacks to the East with just a paddle/wade (not Big Picket). In summer you could also hire sit-on kayaks if you fancy it from the holiday park which would make things easier. There is a lovely inaccessible sandy cove just a little bit East of the main pebble beach.
Some of the stacks don't actually look that hard to climb. Its the getting down again that looks dodgy! The rock is impossible in the wet, and sandy and crumbly in the dry. If you're still tempted, I'd probably inform the coast guard and keep a low profile from the holiday park - although there are no bans, I doubt they'd encourage climbing on the stacks.