Familiar with but not from first-hand experience. As noted above, there have been reports that in order to use EU roaming with a Giffgaff SIM, you may need to use it for a few weeks in the UK first. This is because free EU roaming is technically only for residents, not tourists. (Not enforced by all the mobile companies yet, if ever.) They don't want you to buy a Giffgaff SIM at some crazy low rate and use it all over the EU without ever visiting the UK.

If you were planning to visit the UK for a few weeks first (or not go anywhere else), this might be fine - let you have a working SIM when you get off the plane or something. Otherwise, you could just buy a SIM as soon as you arrive.

We will be in the UK for a week first, then on to France. So you are saying I could use the giffgaff card there as well? Or should I get an Orange card?

giffgaff should work reasonably well here, if you have your phone set for roaming and you're not way out in the boondocks, like we are. Orange would likely be more predictably reliable.

"Orange" is just the new name of France Telecom and has a lion's share of the market in many countries around the world, particularly in Europe and Africa.

I have used them from the start and have no complaints. It should also be pointed out that the EU has eliminated all roaming charges for mobile phones in the EU. Since the UK has not yet managed to slink out of the EU, that is still valid for that country.

In theory, yes. Most EU roaming charges have been abolished. (The UK is still part of the EU for now.) I have roamed with my Dutch Vodafone SIM to different countries without issue. (Not even to the Netherlands yet with it!). But as I said, Giffgaff may not let you roam in France with free roaming until after you've used it in the UK first for a while - maybe more than a week.

But you might as well try it. If the Giffgaff card doesn't work in France or is still not on the cheap roaming, just buy an Orange card when you get there. Understand how to top off the Giffgaff card after you leave the UK too if need be (or top it before you leave). You may have to use Paypal to do it online.