London Underground (LU) has been warned that it could be sued by disabled people if it does not improve access for them by October.
Alice Maynard campaigns for disabled access on public transport
By then the part of the Disability Discrimination Act which governs access to transport will come into force.
Currently only one in seven stations are step-free, which allows entry for wheelchair users.
LU has plans to make another 100 stations step-free by 2020 but needs £1bn from the government to start work.
From October people will be able to sue organisations which do not make their buildings wheelchair-friendly or if they do not have plans in place to make them so.
Alice Maynard, who advises public transport bodies on step-free access, said: "We have been waiting an awfully long time for wheelchair access to public transport and it is coming very, very slowly.
"I expect there will be individual disabled people who want to take action.
"And there will also be organisations for disabled people who are prepared to back individuals to take action against transport providers."
Marie Pye, from the Disability Rights Commission (DRC), said: "The DRC don't really want to end up in court, because in a way it means we have lost the battle.
"We would much rather see LU make the changes and improve the accessibility of the city.
"But if they take the ostrich approach, and stick their heads in the sand, they could well end up in court."
LU's Richard Parry, commenting on the plan to make 100 station accessible to the disabled by 2020 said: "Customers will have within their local area a station that will be step-free.
"And in central London, near to the destination they want to travel to largely, there will be stations that are step-free."