You haven't said why you can't stay where you are, OP. I know it's the end of your lease, but as pp have said, the advice you'd get from council etc is stay where you are, let the landlord evict you. It gives you some breathing space and you'd have your new salary coming in.
I know people who have lived in their cars and they have still needed an infrastructure of friends and family around so they had places to wash, eat, hang out, and so on. They were all doing seasonal work on farms or in the tourist industry, jobs where you could go out and party all night, crash on someone's floor and get a shower at work before you started. Even then, it was pretty miserable and depressing for them.
I think it's an option only if your car actually works - it's not safe to be stuck in a broken down car that you can't move. If the police stop you it's likely your car (therefore your home) will be towed away. At least if it's road legal and goes, you can drive to safe places to sleep. It also means you'll be able to get to your friends and family at weekends, which will give you some relief, allow you to get your washing done and so on.
It will be really, really hard to do a serious job while you are homeless and I think you'd be way better off staying where you are and continuing to search for a place. But if you have to move out, then don't move into a broken down car. At least get a tent on a campsite or in someone's back garden, come to that.