The Income Tax system has one major advantage, and that is that for most people, the PAYE system means that every employer in the country is also an unpaid tax collector, and
most of the administration of the system is therefore "free" to the government (and hence, indirectly, the taxpayer) because employers are doing it and therefore shareholders are paying for it. Some administration and complexity is inevitable if you're to target the effective marginal rate accurately, but it does NOT need to be done through a technically arcane and obtuse system like tax credits.
But the tax credit system is nauseatingly complex to administer (which is why some aspects of it have been horrendously ballsed up by the civil service), with huge incorrect overpayments and then a very aggressive attitude to demanding overpayments back .... or just suspending payments without warning while they claw it back, regardless of whether that's what the recipient was using to feed their family or not. And even where there aren't overpayments, administering it is keeping significant numbers of civil servants in a job .... and the only people that benefits is the civil servants doing it. So next time you here New Labour ministers boasting about how they've cut unemployment, you know where at least some of them went. (that last bit, for anyone that took it too seriously, was largely facetious).