Nope, because we have a 45% top marginal rate that remains flat regardless of income, with deductions below.
so you're back to ignoring that there are other rates again?
the key point with a flat tax is a single flat rate... even with variations of its implementation allowing for a personal allowance, deductions such as when you donate to charity, or indeed allowing other forms of income to go untaxed (such as capital gains, dividends etc..)
we've got multiple bands/marginal rates which apply above our allowed deduction ergo we don't have a flat tax (or a "marginal flat tax"), we don't fit in the list on the article you cited which lists countries with various implementations of what approximate to "flat taxes" and which if you scroll down you'll see doesn't have the UK listed
I'm pretty sure every income tax system currently in use has a top rate of tax, it is rather irrelevant to point out that beyond the top rate there are no further increases that is kind of an inherent property of it being the 'top' rate... it is the existence of multiple rates that make it a progressive marginal tax system rather than a flat tax system. That's the key feature - multiple rates vs a flat rate... and we don't have a flat rate