Yet 7% will mean nothing with an income of £130k.

Why do you think that? 7% of 130k is still 7%. You might argue that someone making that much money can more easily afford the 7% than someone living on 20k, and you'd be right, but people with higher incomes also have higher living expenses.

If we consider this specific law, however, we see the intersection of two common tax trends:

• One trend is called a progressive tax, where those with more money pay more taxes, proportionally. This is done on the theory that the wealthier you are, the more you can afford to pay - going along with your intuition. This is most common with income taxes.
• One trend is called a flat tax, where everyone is charged the same regardless of any factors. This is done on the theory that some services cost the same amount for each person. A good example of a flat tax is VAT.

And so we see that this tax increases as the taxpayer's income does, but the tax doesn't quite keep up with the income increase once you pass 55k-ish.

Why this particular balance struck can only be answered by poring over Parliamentary records and guessing at back-room deals, but it was likely done on the grounds that everyone's health care costs the same (it doesn't, but actually richer people tend to be healthier, so in its way charging them the same as poor people is actually progressive). In fact, if I had to guess, there's a napkin somewhere with a flat number for NHS contributions and a progressive number for pensioners, added together to give the numbers we see here.