You're probably lucky they rejected it. If it had gone through, Amex could have treated it as a cash advance which would have landed you with a 3% fee, interest charges from day 1 and no miles. You only get miles for purchases.

There's a chance if they have an online payment system they might accept 3V prepaid cards which you can buy from Tesco, but it's a lot of hassle to achieve relatively modest amounts (£25 a-time).