What the hell is negative wealth? Is it what people used to call debt? If you have £30K of student debt that is not wealth. You may regard it as an investment in an asset (a university degree) which may or may not result in an improvement in your overall wealth such that the debt is repaid but which ever way you look at it, debt is still debt.
With respect to the taxation of the rich, yes they are taxed in order to pay pensions, for the NHS, defence, policing, etc. But only partially for the benefit of the poorer people in society since believe it or not the availability of pensions, NHS, defence and policing et al is also provided to the rich and let's be clear the poor earning about a certain level also contribute to this at a level that is disproportionate to their income.
Oxfam are right to exclude the pensions and NHS plus all the other state provided elements of wealth from their calculation as these net out at zero in terms of value to all parties (rich and poor). The loss of paying for these items is however far greater for the poor whereas the value of state welfare is far more valuable the wealthy; think tax breaks for buying trees, not using farmland, investing in commercial property, etc. Also think about the tax breaks available for investing in other commercial ventures which mean you get the double whammy of reduced tax and potentially large investment returns.
As for the absurd statement that it is logical that 5 families own more of the UK's wealth than some 20% of the population, why is that logical? Why should it not be 5% of the UK has more wealth than the bottom 20%?
Redistribution of wealth is a bigger driver of progress than ownership by a few will ever be. Those at the bottom should and normally are always striving to improve their lot thus creating demand for goods and services primarily met by large scale industrialization and thus generation of employment and wealth. Those at the top always seem to be seeking greater returns thus generating more automation resulting in fewer jobs or paying of lower wages thus cutting consumption and reducing employment although not necessarily so in the country of low wages.
Wealth inequality will always exist it is something that cannot be changed but the question that Oxfam is really asking is to what should that level of inequality be; where those at the bottom have to rely on charity to feed themselves whilst the rich can pay over the odds for a tin of tuna? or should the inequality be reduced where all people are able to feed themselves to an acceptable level without having to go in to "negative wealth"?