From Sarah's paper:

"But if it is national policy that no one should live below a certain level of poverty, it would not be possible to localise the benefit system, as given discretion some councils might withdraw payments."

The test certainly suggests that national government ought to be able to set a national safety net below which no local authority could provide, but surely there is nothing to stop local authorities from going further if they wished?

While not a benefit, an immediate example springs to mind: the national minimum wage. Why can't we have a London minimum wage (or a Kensington one for that matter) if that's what local people want?