Actually, the most relevant statistic (which is, of course, much more difficult to calculate) is how much tax each pay relative to their disposable income—ie, the amount left over after necessities such as food, shelter, and clothing have been paid for.
With any vaguely reasonable calculation of this, it becomes painfully clear that the poor pay far, far too much (because they have, effectively, no disposable income) and the rich pay far, far too little (because almost all of their income is disposable).
However, disposable income has a technical meaning. When the ONS publishes disposable income statistics, they mean income remaining after tax (I presume they subtract income tax and NI, but not council tax because that's local). They don't subtract e.g. energy bills or food.
From where I sit, "income after tax" doesn't really seem to fit as the meaning of "disposable income", though I suppose I can see why it would look that way to an office like ONS.
Now, to be clear, "where I sit" is in the US, and I've never seen "disposable income" be given an official usage like that over here; its only meaning that I've known is, much more colloquially, just what I said: the amount of money you have left over each $timePeriod after paying for the basic necessities of life. (How one defines those, specifically, varies greatly from person to person.)
With any vaguely reasonable calculation of this, it becomes painfully clear that the poor pay far, far too much (because they have, effectively, no disposable income) and the rich pay far, far too little (because almost all of their income is disposable).