Going underground

My Flat Coated Retriever is too big to carry, so if I use the London Underground I need to plan a route across London that avoids escalators.
Is there anywhere that lists tube stations that have either lifts or stairs? I guess wheelchair users will have similar problems - finding wheelchair friendly stations would help.
Where can I find dog-friendly Underground stations?
Gita Beecroft, via Twitter

Transport for London says…
If you travel with a dog on London Underground you must carry it on moving escalators. This is for the safety of the dog as it could be seriously injured if it gets caught in the moving components of the escalator.
If your dog is too big to carry, you can use TfL’s Journey Planner http://journeyplanner.tfl.gov.uk/user/XSLT_TRIP_REQUEST2 to plan your journey using public transport and avoiding escalators. The Journey Planner tool can be found on the right hand side of the home page of TfL’s website, www.tfl.gov.uk.
The ‘Advanced options’ include a choice of mobility requirements to be taken into account when planning your journey. By ticking the option ‘I cannot use escalators’, Journey Planner will return a list of travel options avoiding escalators. These recommended routes will only use London Underground stations which have stairs or disabled access.
Journey Planner also takes engineering works and line closures into account, so checking it before you travel will ensure that you know the best route for that day.