It is up to you to ask for a remark and to pay. You ask the school for a form and fill in it and then they process it, as they were the examinations centre. It does have to go through school.
Schools sometimes put in for remarks themeselves, but this is rare, because if you are remarked, the new mark counts and it can be lower as well as higher. So schools don't want to risk pupils being downgraded generally.
When schools think everyone has been wrongly marked, they will usually put in for one or two remarks, of candidates who are not near any grade boundaries, so for whom a downgrade of actual grade is less likely. They will only ever do this with the knowledge of the pupils.
If the school find a few remarks rise (perhaps ones which were put in for by pupils....school always informed of outcome) they may decide to complain and if a certain percentage of papers have been raised,the exam board will look at the whole schools papers again.
If your mark changes, your fee is refunded.
Most remarks do not result in an increase in marks. Those that do, often don't lead to a change in actual grade. Exam board remarkers are under pressure to not change marks. A certain level of difference in marking in essay type subjects is allowed (called tolerance) so if the remarker thinks the original marker was within tolerance (often just a couple of marks) there will be no change in mark. Lots of papers will see increases in marks, but they are a fairly small % of the total remarks.