It is my understanding that English Common Law still prevails in this situation and any damage claim has to prove negligence on the part of the providor to be successful. Unlike the USA, the user also has to accept responsibility for their actions - minor damage in a parking facility is a self-evident risk which is beyond the reasonable control of the providor and the user is deemed to accept responsibility by using the facility. After all; the user has the choice of parking elsewhere albeit possibly at some inconvenience if the facility is not suitable.
IMHO, the best way to get action is to not use the facility or patronise the business whilst encouraging others to do the same - nothing like a loss of profit to encourage corrective action