The U.K. government hasn't always, now or in the past, spent a lot of money policing the welfare system. With any welfare system, there will be people who try to get around it, cheat it, and use it when they don't really have a need. But that tends to be a very small percentage. Arguably, the U.K. system and many other systems are over-policed, in that the cost of prevention, of catching people getting the benefits who should be working, far outweighs the actual gains derived from stopping those people. For the overwhelming majority, if the welfare system is inadequate to prevent poverty, increasing the amount of benefits available will have a major impact on alleviating poverty. It will have a minor impact on increasing a very small number of people who'd beat the system and cheat it. This is true not just for the U.K.; it has been demonstrated in many comparative studies in many countries.
The figures just don't stack up when you look at objective social science research, whatever the underlying political beliefs of those researchers. In most systems, increasing the welfare benefits for an adequate system will have an impact.