Unless a school thinks there has been serious mis marking across the board for their students, and considers steps towards a full review (which will need some individual uogrades first) then it is very usual for parents to have to pay.
Schools pay for kids to enter the exams. It costs a lot and they are strapped for cash. Parents have to be responsible for funding re-marks as schools simply can't afford it - they will never tell a child they must get a remark, but they might advise it, but also have to point out the risk of being downgraded too, so in the end the parents have to take responsibility for the choice and the risk....schools won't out in for remarks without parental consent, partly because the risk of grades going down.
It is true that those with less money are disadvantaged here and might lose out on higher grades. In Independnet schools, parents after advice from staff, often request numerous remarks, and of course if you don't put in for one, you certainly aren't going to get upgraded. However, this alone doesn't mean schools should pay for all remarks - remarks are always, extra, optional expenses, not part of the general curriculum, so if you want these extras you have to pay, in the same way that if you want extras like violin lessons you have to pay....not an equal world, but how it is.
If exam marking were reliable, all of this wouldn't be an issue, but it is unreliable. What I would say, is that if the school has suggested they think a serious error in marking is likely, it's really worth finding the money to pay for a photocopy of the script - cheaper than a remark, and then teachers can look at it and decide if they think it really has been significantly meanly marked, and if they really think there is a strong chance (not just a hope that with a following wind a an extra mark might be found......marks are only changed now when the marking is wrong enough to be in the wrong band) then it's probably worth finding the money for it.
Yes, it would be good if you didn't have to pay as parents.....but here, it's a choice to either pay up and perhaps get your child a better grade, which might make a difference to their future - especially important if making the difference between a pass and not a pass, or not paying, through either principle or genuinely not being able to afford it or scrape that money together (a reality for some people). As parents we pay for all kinds of things for our kids, and even if we think the state should be funding it, if the school says they really think there's been a serious mis mark (and again, not just that they are chancing their arm) then I'd see this as just another expenditure needed by kids....and probably one of the more worthwhile ones.