The charity recently carried out a survey of disabled people aged 18-65 in the UK to show the barriers faced when trying to travel by train.
These included being unable to use train stations because of a lack of step-free access, to feeling trapped in the carriage, or not being made aware they are at the right stop.
Mr Maynard said, who recently received the Which? Positive Change Award for his work as Rail Minister, said: “I have long campaigned to improve accessibility across the rail industry. I launched the forthcoming inclusive transport strategy and drove forward an ambitious agenda across the Department for Transport. Change is happening but more can be done.
"Public transport is a vital part of life and the Government must continue to make it a priority to ensure train operators provide accessible end-to-end journeys.”
Neil Heslop, Leonard Cheshire’s chief executive said: “It’s unacceptable that in 2018 disabled people cannot travel independently and easily whenever they want to.”