Guys, thanks for letting me know about Amazon. I tried it this morning with a Visa card, and it was fine, so the issue must have been with the Maestro card. This will make all future birthdays and Christmasses so much easier!
(although, my ultra-picky family are a bit sniffy about gift cards... they kind of feel it's what you get someone you can't really be bothered about, but surely they can understand the predicament of being abroad, and if they can't... tough.)
I had been looking at other options... in Texas they have this fast food place called Sonic, which my family really like, and I was on their website trying to sort out gift cards. It looked like it might work, but then, although it allowed me to enter UK as the country of my billing address, it wouldn't let me bypass the 'state' field, and kept rejecting because of that. Then I tried to email their customer service, and it was this huge long convoluted series of questions about which store I was at, what time of day, was there a manager present, etc... so I gave up.
Starbucks was also a thought, but I hadn't got as far as trying to navigate their website. Might think about that one for my niece's Christmas... she is almost 16 and seems to think coffee the height of sophistication!
Would love to hear other tried and tested ideas, if anyone has any...