"It's obvious that the top five families will have more than 20 per cent of all Britons. Do they think we all just got off the turnip truck or something?"
Actually, this is not obvious. In fact, if the Lorentz distributions that Gini uses were correct, this would certainly not be the case. For a Gini of 0.33, the bottom 20% owns/earns 4% of the total wealth/income. For the top 5 families of the UK (~ the top 0.00001%) to earn more than that, the Gini coefficient would have to be very close to 1.
That is the point of the Credit Suisse report that the Oxfam numbers are based on. The Lorentz curves heavily underestimate actual discrepancies in the wealth and income distribution. This goes a fortiori for the after-tax distributions. This is what all the recent hubbub is about: there is a top echelon in our societies that is extremely rich, and hence extremely powerful. There is more than a whiff of ancient regime here, and it is dangerous. It is dangerous for the rich, who may find themselves targeted. It is dangerous for the politicians, who may find themselves stuck between assuaging populist anger and preserving the financial backing they need. It is dangerous for our economies, because - unlike the ancient regime - the rich are globally mobile, so their interests are even less aligned with those of their local economies.
In short, you don't understand why there is an issue because, well, you either don't read the reports or you fail to grasp what they mean. Oxfam may be a peculiar champion for equality in developed nations, but it makes some sense: they know very well how wealth disparity on a global scale can keep vast swathes of the world in dire poverty. Maybe they should focus on fixing the global problem rather than the local one, but perhaps they concluded that developed countries are too much in thrall to those who benefit most from the global inequality. In any case, if you don't understand the message, don't shoot the messenger.