Taylor Woodrow will carry out the £75 million overhaul of the central London station, which has five Tube lines running through it and will be a key hub for ferrying passengers to and from the Olympic site in east London.
LU had originally planned to ensure the whole of the station had step-free access but this would not have been carried out in time.
The easier access will now be created only on platforms 1 to 6 for the Metropolitan, Circle and Hammersmith & City lines.
The deeper Jubilee and Bakerloo lines could get stepfree access after 2012 but no plans have been finalised.
A Taylor Woodrow source said: “There was originally an option in the design for a lift to take people to the level below the Metropolitan.”
LU is also seeking a Transport and Works Act Order to ensure the job can start on time as construction on platforms 5 and 6 involves work that LU does not own or control.
The TWAO, which will authorise the compulsory acquisitions of the necessary land, will be applied for in December with a view to receiving permission to go ahead by June 2010.