My mate manages the parking wardens in a town near me.
His advice - morality aside - is always appeal.
He says this because the local authority has allowed several appeals on what he considers very flimsy grounds.
A fixed penalty ticket from a copper for a moving traffic offence is a more serious matter, but I don't see how the penalty can be increased on appeal if, like a parking ticket, it goes to a tribunal, although it may well be upheld.
If the 'appeal' is effectively a not guilty plea and a request for a hearing in the magistrates court then the penalty could be increased - no credit for pleading guilty - and you may have the other side's costs awarded against you.