Note from the other perspective - I am a landlord (not actually planned - I bought a flat then 6 months later met my husband, moved in with him and due to housing market renting was a better option than selling).
I rented to a single mum on benefits - at first wasn't sure cos of all the stereotypes but then thought ok, she has references and a guarantor so i'll give her a chance.
1st month fine, second month rent was late - she blamed the council for changing the date that the housing benefit was paid but only bothered to mention this the day after the rent was due.
For the rest of the tenancy she made promise after promise of paying the back rent that she owed and didn't pay anything. Time came for her to move out and guess what, nope she's still there.
The council have actively TOLD her to say there (at the date the tennancy was up she had just had another baby - well the first was going to school so she was being expected to get a job!) but tennant didn't inform me of this. This was in October. The council promised that she would be out within 2-3 weeks, she's still there and i'm having to pay for legal action and probably bailiffs to get her out.
Unfortunately, stereotypes are sometimes there for a reason and she has meant that i will NEVER rent to someone on housing benefit again (single mother or not) due to the complete lack of responsibility that the tennant has shown and the councils actions.
All the reasons above about the claw-back and increased insurance are correct, but, i'm sorry to say, some of the blame for landlords not renting lies with some single mothers on benefits who have been seriously bad tennants and people are too scared to risk a hell of a lot of money on them.