Whether the UK is too unequal or too equal is not something that actually has a certain answer. Sure, we can posit that some of the things we do to reduce inequality might make us all poorer (and some of the things we do do) but what is the "right" amount of inequality is something that's up to the moral precepts of each observer.
However, what we can do is make sure that we understand how much inequality there actually is. That figure above comes from here. My thanks to Christie Malry for pointing it out. And yes, of course the ONS is telling us the truth here. It might well be that you think that the original inequality in the UK is unfair, something that should be changed. That the top 20% have 15 times the income of the bottom 20%. But do note that things are indeed done to change this. So much so that the final inequality, after all taxes and benefits are accounted for, is only 4 to 1. It's even possible to think that this is still too high but everyone should be able to agree that it's very different from 15:1.
Malry has named my repeated insistence that this difference matters "Worstall's Fallacy". We can't make decisions on whether we should be doing more about something unless we look at the effects upon whatever it is of what we're already doing. We need to know how much we're already changing income inequality before we can demand that more (or less) be done. The same is true of wealth inequality, people living under the poverty line, even the concept of the Living Wage (where the only difference between that Living Wage and the current minimum wage is the amount that we shamefully tax off those earning low wages). We muct look at the current end result before deciding upon any future action. BTW, the TUC did a very similar exercise a couple of years back but looking at the top and bottom 10%s rather than quntiles. Inequality of market income dropped from 30:1 to 6:1 in their results.
We already do a great deal to reduce income inequality in the UK. And the only way we can possibly decide upon what to do next is by acknowledging that fact and discussing whether, after all of the taxes and benefits, we have too much or too little income inequality.