I think this is a very difficult situation with no easy answer.
There are a number of LLs who do take on DSS claimants, but finding one in your area might prove very difficult. Transport seems to be the key, both for a property and for finding a job. It might be worth considering using the money you have saved to take driving lessons (I'm not sure how far £600 - £800 goes these days with driving lessons?) but you may find it a good investment as it will make you a lot more flexible in the job market. Once you get a job, getting a rental property will be much easier.
I'm not sure about your mother's attitude, unless there's another problem there that you're not saying?
It just seems to me that if you had transport you might even be able to get a menial job (no offence meant) such as working at a supermarket etc to get you back on the job ladder and get an income.
At the moment, sinking all your money into a deposit on a property seems to have few benefits. Apart from the rent (which would be paid in arrears to the LL, if you can find one) there are a lot more other expenses in running a home. Where would you get the money at present to cover all these bills?