mmmm....I'm not very well clued up on the various credit cards and what you can hold simultaneously, but if you can't refer friends/relatives with the card you have I would suggest you get an Amex Gold Card and pay three family members their annual fee of £70. Total cost would be £210 for them and £70 for you. If you know some higher earners that might be interested they could get immediate approval online. Your account would be credited 12,000 points per person, which you can convert to BA miles in a couple of days. If you are cute the whole process could be done in a week.
I would of course be happy to refer you for a Gold Card, if you are interested PM me!