What's the best international phone plan?

Vodaphone "pay as you go" sim would be best. You can get a freedom freebee which allows you to add differnt packages to your phone to suit your needs - ideal for UK and Europe but rate will be slightly higher in Ireland. You can add a freebee for internation minutes too if you like. Otherwise next best company to look at is Virgin.

If your phone can take any sim. It's very easy to buy a sim card in most newsagents. Most of the time they come with some credit. If you are calling with in the uk it will be cheap. I think giff gaff is a cheap one that you can pay upfront for the month for unlimited.

I would just get a pay as you go SIM card, there's a kiosk in London Heathrow Airport and they have several options so you'll be able to find something that suits your needs.

Get GiffGaff, they specialise in cheap, no commitment plans. A lot of my international friends are with them, when visiting the UK. I personally haven't used them, as I'm on contract with a different company (but I live here)