Please bear in mind that 80k is taxed at a higher rate than 25k.
I don't agree with Seldon's idiocy either. I think state schools should be available to all because we are supposed to be a cohesive society, and there are obvious problems with leaving state schools available only to the poorest in terms of what will then happen to those state schools, even leaving aside the issue that richer families have paid for those schools via their taxes several times over. But having said that: tax bands are the exact same for everyone, in that earnings above a band are taxed at the higher rate and earnings below at the lower. We all have a personal allowance a little over £9k which never attracts any tax; then we move into a further band which allows another £32k attracting 20% tax, and then people lucky enough to be getting over £41.4k pay 40% tax, but ONLY on earnings above that £41.4. We all pay the exact same tax levels within each earning band.
Everyone is entitled to the same tax bands for each step of earnings, it's just that the majority of the country are never in a position to find that out. Someone on £25k pa salary is not lucky enough to ever reach the higher tax rate, but everyone's £25k is taxed at the exact same rate - whether it's all you earn, or whether you're on £150k a year. Higher tax is payable only on earnings in excess of the threshold, NOT the full earnings.