What are the various UK and mainland-europe SIM card companies?

I've got an unlocked Android phone in anticipation of my imminent move to London and then down the line to mainland Europe as well. For now, I've got a prepaid US T-Mobile SIM card in it, but obviously upon my move to London I'll want to use a different prepaid SIM card there, and also various prepaid SIM cards throughout Europe depending on the local area I am frequenting. Yes, I know it's going to be difficult for other people because my number will be constantly changing, but that's sort of the point-- I enjoy being stealth. ;) Can anyone recommend a RANGE (i.e. not slanted towards one or another company exclusively) of EU-wide carriers to consider using the SIM cards of? Thanks.