Honest answer - don't think about getting more credit until you've paid off what you've already got. If you've already got a car then unless it's costing a fortune to run (by which I mean it needs a new engine) keep it going until you've made some inroads into your existing debt. As you've already worked out loan providers are likely to think that you've already got too much credit now and will be unwilling to give you any more. You may be able to get car finance as that would be secured on the car.
Concentrate on sorting your debt out first and save the £300 a month until you've got enough to buy a good second hand car - you shouldn't need more than £2,000 - which won't depreciate much in value and keep going until you can save for a better one. I assume you're already saving the amount you'll need to pay off the interest free card before the interest free period runs out ? If so then save the extra in the same place and you'll be surprised how it mounts up. See if you can make overpayments on your personal loan as well as that will save you alot in the longer term.