When you park on any privately-owned car park, you're automatically entering into a contract with the owner of that car park (or the company that the owner employs to operate it) to pay any 'reasonable' charges that are clearly displayed upon entry. So, if
(a) there are clear signs at the car park, telling you that a charge of £100/£60 will be levied in respect of any vehicle not correctly parked within a bay ; and
(b) you parked your vehicle in such an incorrect manner ;
then you're contractually obliged to pay up.
If you fail to pay then, just as with any other unpaid debt, the parking enforcement company can use the small claims process to take court action against you. That could end up costing you a lot more than the £60 charge that you're currently facing.
Several people have tried to win court battles against parking penalty notices. Stephen Thomas was one of the first, back in 2008, but lost and ended up having to pay more:
https://www.rochdaleonline.co.uk/news-features/2/news-headlines/15278/judge-enforces-parking-penalty-in-landmark-case
Barry Beavis took battled all the way through to the Supreme Court in 2015(almost certainly costing him many thousands of pounds) but he also lost:
https://www.itv.com/news/anglia/2015-11-04/essex-chip-shop-owner-vows-to-fight-on-despite-losing-supreme-court-parking-battle
It would probably be best to pay up!