They are called 'reviews of marking' these days and A Level reviews are fast tracked.
The idea of calling them reviews was essentially to discourage them and to persuade schools - and parents and students- that there was a low chance of getting a grade changed. This is because chief examiners look at whether the mark scheme is correctly applied , rather than quibble over a few marks.
However - notoriously- when our lot were year 11 , huge numbers of Eng Lit GCSE grades went up as a result of these 'reviews'. It made me cross , actually, because many state schools cannot afford to fund these reviews , so focus on a narrow (overall data helping) range of students and, therefore, affluent parents and well funded schools win out. Not great.
Politics aside, though, I'd always encourage parents to give it a go. With the caveat that marks can go down (this is rare but it does happen)