The Guardian has put together this list of the best whale watching locations in the UK. It mentions the follwoing sites.

• Moray Firth: as was shown on Springwatch you can watch the most northerly known population of bottlenose dolphins right from the shore – often only a few feet from the shingle. No binos needed! The best place to view them is Chanonry Point on the Black Isle. Humpback whales can also be spotted in the outer Moray Firth. Visit seawatchfoundation.org
• The best place to watch Killer whales is the Shetland Isles, especially at Esha Ness. They are becoming commoner.
• Isle of Mull – minke whales. Mull was the first place in Britain to offer dedicated whale-watching More here wspa.org.uk
• Cardigan Bay has a population of 130 bottlenose dolphins which can be seen from the shore at New Quay. The pods feed here from April to September.
• St David’s Head in Pembrokeshire: dolphins and possibility of fin whales in the summer.Here new-quay.com
• Common dolphins can be seen at Durleston Head in Dorset.
• Sites in Cornwall: Lizard Point, Gwennap Head and Cape Cornwall for dolphins, pilot, killer and minke whales marinediscovery.co.uk