We did the boat from the Westminster Pier some years ago so my memory is not acute.
My recollection is that there are wide stairs from the Westminster Bridge street level to the quay level then ramps to the pier. You could correspond with one of the boat service companies about lift access to the quay level.
We rode the boat downstream then walked under the river for our return via Docklands Underground. The tunnel is handicapped accessible with both stairs and lifts at each end: http://www.royalgreenwich.gov.uk/info/200102/walking/693/foot_tunnels
London disabled resources:
Around a quarter of Tube stations, half of Overground stations, most
piers, all tram stops, the Emirates Air Line and all DLR stations have
Many boats have boarding ramps to give step-free access.
Guide to River Thames boat services A guide to fast and frequent river
services as well as leisure services with maps, timetables, fares
information, places of interest and useful contact details. Available
in large print and audio. You can also download the River Guide (PDF