It is partly the debt but more that my credit is rubbish so buying a house and saving is out of the question.
Hang on, I think you're getting a bit ahead of yourself here!
Once you get to grips with your debt, your credit rating will start to improve. That's why throwing as much money as you can at the smallest debt, until it's cleared, is such a good idea. There's loads of advice on MSE about building a credit score, but you need to get a handle on the existing debt first.
I'm unclear if the £600 of disposable income you have each month ispartly going on the credit card repayments, or if they're included in the £300 a month "bills" money. I'm guessing not, in which case the £300 on bills seems high. Have a look at what you can reduce here, eg Sky, phone contract (if you're due an upgrade soonish, for example, you could hang on to the phone and go sim-only, that could be a big saving).
If you managed to save £50 a month on your bills, and paid down your smallest credit card debt with it, you would see the balance start to reduce much more quickly.
A significant chunk of your income goes on your car. I know it's essential for your work, but are you making sure you claim back every penny in mileage that you can? I found when I actually clocked my mileage using the trip counter, rather than just relying on knowing fairly accurately how far away places were, that I was massively underestimating how many miles you can do driving round looking for parking spaces. (And shop around for your insurance at renewal time, and try and put a little aside each month so you can pay it upfront, then that £75 a month can go to paying down debt).
One exercise that clients find an eye-opener is not to buy anything that isn't essential for a month. They're always gobsmacked by how much of their spending is on stuff that they don't actually need, or where a purchase can be deferred. I know how easy it is to feel the need to treat yourself when you're depressed, but it's a very short-lived mood lifter and has a hangover in the form of no money, which just brings you down again. I bet you'd find an awful lot of your spending is discretionary.
If you can apply the same sort of discipline to your food shopping, and only buy what is absolutely essential (lots of veg, no chocolate, cake or biscuits) you may find that you start to lose weight, too!
I've been where you are, OP, and I know how it feels utterly impossible to see a way through the mire. But once you've made a small change, and then seen a benefit from that, your motivation improves no end and the next, bigger, step is a lot easier. And making that first step will help you feel more positive, too.