You would get cheaper repayments on the credit card debt if you managed to get a 0% deal (as you wouldn't be charged any interest) but you would have to pay about 3% of the debt as a balance transfer fee. For as little as £1,200 I doubt it would be worth it - much better to try and repay as much as you can each month by cutting back on everything possible. You only need to find about £150 a month (depending on your interest rate) for the next year to repay the balance - you might even be able to save some of this by simply checking you're on the best deals for your utilities.
I doubt you could get the car finance transferred to a 0% card. You could try for a loan to clear it but the interest rate on car finance arrangements tend to be low because the loan is secured on the car so if you switched you'd end up paying more interest which is more expensive in the long run. Have you approached your loan company about selling the car and using the proceeds to settle the loan ? If you have paid more than 50% of the original sum you may find you can hand the car back to them in exchange for the loan being cleared. Then assuming you can get to work cheaper by public transport you'll ahve some extra money to pay off the credit card even quicker.