August is getting late, May June and July are the peak and the south coast only really seas the odd bird passing through as they migrate back out to sea from the North Sea. The nearest place will be either Lundy on the North Devon Coast (great place but a 2 hour boat ride each way and Puffins are limited to one cove in the main) or Skomer in Pembrokeshire is the place down this end of the world..
It's a few hours drive but you'll have Short Eared and little Owls to view if the Puffins have all moved back out to sea.
You may be better off going after the Red Squirrels if you're based in Dorset. Or drive up to the Somerset Levels for a variety of Birds, Corfe Castle, Portland Bill, Chedder and Glastonbury for Landscapes.