The UK is easy. Walk into any mobile phone shop, select your PAYG (Pay As You Go) plan, pay - cash or credit, it's all the same, 3 minutes later you're outside and good to go. No credit checks, no wanting to see your passport, no wanting your telephone number or a UK address, no wanting to know what you ate for breakfast. In the UK, mobile 'phone competition is stiff and there are lots of great deals. You'll have no problem at all. All they're interested in is your money!! It's completely deregulated.
In France, Members report it's a different matter altogether and very time consuming and problematic. Most have decided to abandon it and go for WiFi hotspots.
Tim