Well, I've never been to mainland Greece, but I can highly recommend the islands. I've been to a few, and they were great. Kos is especially nice, I had a lovely time when I went there a couple of years back. You can get boat trips to Bodrum in Turkey, which is cool, you get to haggle with all the pervy men in the markets!
As for what to pack, if you're getting into London in May, I would suggest you should be prepared for any kind of weather! Hopefully it will be starting to get warmer, but unfortunately, you never know. It might be worth bringing something a bit warmer. If it rains, you can always buy an umbrella while you're over here.
Places like Greece and Italy will probably be really hot around early-mid summer, so be prepared for that, with sunscreen, etc.