Actually, I just thought of another option. This might be workable.

Half (at least 1/3) of the western steps could be removed and replaced with a small lift. It wouldn't be enclosed like proper lifts, just an hydraulic platform with suitable safety barriers around it. The east side could use a ramp - with a bars to obstruct bicycles and a safety handrail on both sides.

The lift would be expensive and probably break a lot. But this scheme is doable and would benefit all "movement impaired" and those with small children in buggies.

Get TFL to build it and add an oyster card reader! PAYG system hahaha!