You should transfer to a 0% interest for X-months credit card.
You will be charged a 2-3% fee, but this is likely to be less than the interest you are currently paying on your current credit cards.
E.g. say you are paying 18% (pretty standard interest rate) on your £10,500:
You pay off the minimum, say 5%? = £525, plus the extra £100 you pay, = £625
That leaves you with a balance of £9,875.
The interest you pay on that (at 18% p/a divided by 12 to get monthly interest rate of 1.5%) = £148.
Your balance is now £10,023.
Next month, you pay off the minimum again: = £500 + £100 = £600
Balance = £9,423.
Interest on that: £141
Balance now: £9,564.
That's 2 months.
If you tranfer to 0% for, say, 9 months at 3% tranfer fee on your £10,500, you'd pay £315 once. Total £10,815. But then you'd only have to pay that, and wouldn't be accrueing interest for 9 months. It would cost you about £300 in interest in just 2 months, so over the course of 9 months, you would "save" (or rather stop racking up interest) about £1000 (I think).
Then, at the end of that card, transfer again. Again, you'll pay the fee, but it is likely to be less than the interest you'd pay on your debt on a normal CC interest rate.