Surely this can't work without some aultrism involved? I find it doubtful that any alumni can get 10k of benefit from the increased reputation that a 10k donation can provide.
Declining marginal utility, and how rich the people who tend to make big donations are, play a role here.
If you earn 50K, you net 37640. 51K and you get 38220.
If you earn 51K and donate 1K, you net exactly the same as if you just earned 50000. i.e. 580 less than if you had just kept it (If you had put it in your pension instead, you would have kept the whole 1000)
There may be some circumstances where it makes a difference, where certain thresholds could be crossed, but AFAIK, the way they all taper prevents that.
You can only get a tax break on 40K of pension contributions, so if you earn 91-101K and claim child benefit, without another pre-tax vehicle to soak up the rest, you'd have to pay the clawback charge. However, I doubt that would work. With 3 children you'd have to donate 10K to save about 2.5K.
If you earn something around 300K, it might do something because of the tapered pension allowance. Again, I doubt it. At 250K, if you donate 10K, you can put an extra 5K in your pension. Above that, I don't think there are any more thresholds.
A number of schemes exist around various countries to promote incentives to donate, and they typically end up with people paying less tax overall than they would otherwise. (Note: I don’t think it’s a bad thing, no critique meant).
In the illustration in your link, Sue gives 1k to charity, and as a result, and pays 350 less tax. This means that, as a result of this donation, her net income has fallen by 650.
I did not provide the specific names of all the rules, but I thought that would be obvious from the numbers, context, and some of the terms
I had not considered the difference between payroll giving (my first example,give 1k before tax, charity gets 1k, your taxable income is 1k less), and claiming back (you give 1k after tax, charity gets 1.25k, you reclaim some of the tax you paid), but payroll giving is more efficient for the donor, as they pay zero tax on the donation, rather than basic rate, as in the reclaim method.
There is no UK legislation, as far as I know, that reduces your tax bill by more than your donation.
The schemes amplify the effects of existing altruism, rather than offering incentives to persuade non-donors to donate.