You are entitled, under the RTA I believe (or perhaps under the
aprking regulations for the particular city) to make a claim for costs
only if the issue of the ticket or the councils refusal to allow your
appeal (I cannot remember which) is "frivilous, vexatious or wholly
unreasonable." Whether their behaviour is regarded in this category
is the decision of the parking adjudicator, who you will appear before
if the council refuse your appeal.

IANAL, only someone who has successfully appealed to the Parking
Appeals Service.