The charity's Chief Executive Peter McCabe was joined by Robert Halfon MP, as well as representatives from FairFuel UK and CLIC Sargent to hand over the petition which attracted more than 25,000 signatures.
Parking is already free at almost all the hospitals in Scotland and Wales, but in England people are still forced to pay.
Peter McCabe said: “When a brain injury strikes, families are anxious to be close to the bedside of their loved ones, particularly when in critical care or in a coma, for example.
“Treatment can last many months, meaning the daily costs of parking can reach into the hundreds or even thousands of pounds, putting immense financial pressure on families at a time when they are shocked, bewildered and vulnerable.
“Every day our Emergency Fund hears from desperate families who are struggling to meet the costs of hospital parking. For instance only last month we heard from a single mother who had been driving over 34 miles return trip every day to be by the bedside of her son who was fighting for his life in intensive care following a assault. Due to the high costs of parking she was struggling to pay her utilities bills and stay financially afloat.
"It's clear that excessive parking charges punish families who are already trying to cope with the most difficult of circumstances and the government must act now.”