Free Traffic Legal Advice

We recently booked 2 weeks parking with a company called Heathrow Meet & Greet (heathrowmeetandgreet.co.uk). On our return we received three parking charges on three separate occasions during the period of parking. When we queried this with Heathrow Meet & Greet they denied any responsibility, saying they subcontract the services to 3rd parties. They provided an email address from which we have had no response. Following appeal, the council concerned refused to waive the PCN advising us to take it up with the parking company. We have been unable to contact the company who had the use of our vehicle for this period.
Could you please advise what stance can we take with a) the parking website and b) the council who rejected our appeal?
Thank you in advance.