I think "rare" steak is very different in the UK to over here. If I remember well, you could probably go for medium and still be fine, but if you are worried in any way then best to go for well done.
I have already had this problem over here. I obviously don't have a bump yet, so get really annoyed looks when I ask waiters for really specific things. I ordered a burger a while ago, and asked for it "well done. No wait, I would like it BURNT please. No I'm not joking."
When he brought it over he made this big flourish about it being "SUPER well cooked borderline burnt!!". It was still a bit pink inside. I still ate it, though next time I might pull out the "BECAUSE I AM PREGNANT" card. Or just avoid it.
The french do not understand how to actually cook meat!!! (unless you prefer it pink).
Well cooked is medium
Medium is rare
and rare is raw! 