The HateMail have also conveniently overlooked that most (all?) of the money he was receiving was not in benefits meant for him.
He was forcing the 2 women to pay their wages, and the tax credits they legitimately got (and needed) to supplement their low pay, into his bank account. (As an aside, I am interested in how it was possible for him to be paid their benefits - would they have been receiving them in cash, or what?). And as for the child benefit, that was obviously meant to be paying to help support the children.
However good your welfare system administration, you can't easily force people to spend the child benefit on the children, or prevent them from handing over their own cash to someone else once it's received, without becoming very intrusive.
Unfortunately, a man like him would take advantage of anything he could, including this fact. But trying to prevent that by cutting back benefits would a) only penalise the people who actually need the benefits (like those who ARE working but don't get a living wage, or children) and b) would almost certainly just lead to him taking other, equally nasty paths* to get money - if he hadn't been creaming off their benefits, I could just see him taking up a new career as an armed robber or something - or even more likely, taking the safer option of forcing some of his women into prostitution (anyone wondered whether Mosley paid for their services?).
*to clarify, with "equally nasty" I am talking about what he was trying to do, i.e. getting his mitts on all the benefits, not the children's deaths of course which was obviously much worse but not what he intended (even if he should have been able to foresee the risk...)