Let us imagine that you are concerned about the amount of inequality there is in UK society. You wish to reduce said inequality. I might not (in fact don't) share that concern but even as the interested amateur that I am as an economist (ie, not an economist, simply an interested amateur) I might be able to offer some guidance as to how you might do this.
The first observation would be that some countries have indeed lowered inequality (and relative poverty) so to reach your ambition (which, remember, I don't particularly share) we could go and look at what they have done. The poster children here are of course the Nordic countries. And the most important thing we can say about their taxation systems is that they are very differrent indeed from what is usually proposed here:
....the countries that have been the most successful in reducing inequality don't have particularly progressive tax structures. The real gains in reducing inequality are achieved by means of well-designed transfers.
Indeed, the Nordic tax structures are not particularly more progressive than the one we currently have in the UK. Yes, they have high marginal income tax rates but they also tend to have lower capital taxation, lower corporate taxation and higher VAT than we do. That is, they have concentrated on growing the goose, taxing consumption more than we do, so as to provide the revenues to make the transfers.
Which leads us to the ritual calls here for the rich to be paying more tax, for companies to pay "their fair share" and so on, that our tax system must be made more progressive. But why, if we know that the way to reduce inequality is not through the tax system at all, should we do that?
Shouldn't we be copying the systems which really do reduce inequality?
As I say, I'm not an advocate of this inequality reduction in the first place. But for those who are there's something very odd indeed about their insistence not to do what has worked elsewhere: cut corporation tax, cut capital taxation and raise VAT. Why is that?