However, complete redistribution still wouldn't solve Oxfam's definition; they use 'disposable income' as their term, and, as some people consume more resources in the form of utilities (heat, light, etc), then their bills will necessarily be higher and those people will still have a lower disposable income.

You'd have to regulate to everyone an equal amount of heating, lighting and so on, into perpetuity, irrespective of their personal requirements or wants.