I agree with Pat.
Both Koh Tao and Similan Island are the best places for Scuba Diving. For shopping I would actually recommend Bangkok if you have time (say on your way back before flight back to London) otherwise here in Phuket there are also many areas for shopping depending what you're looking for.
Phuket also offers bungee jumping although it is nothing extraordinary. You jump from a crane with a lake beneath you. I strongly recommend Krabi. Beautiful area for seightseeing and climbing (i you like that).
And here in Phuket you always have Patong for a good time out at night!
Hope you'll fully enjoy your holidays.
Let me know if you need more help.