In answer to your P.P.S: Three seems to be a very good options in terms of Prepaid/PAYG. It offers 3p/min calls/2p/min texts/1p/mb data which is good for the UK. There is a lot of public wifi in London, the ones that I use mostly are Starbucks and London Underground Wifi.

If you want to call abroad, take a look at dial-a-code which will reduce your rates considerably, however this won't cover your trip further on into mainland Europe. I would imagine a company like Lebara or Lycamobile which are known for their low-cost rates in most places in the world would be able to help you out.