Very few, if any. They may not have escalators (Covent garden, for eg., but no-one in their right mind uses that - just use Leicester Square and walk on the street) but there are almost always ways of getting up to the street, and assistance is signposted for people with problems.

> platforms are often at a significant offset from the underground cars

Not sure what you mean here - mind the gap? Typically less on the Piccadilly than some other lines - Bank on the Central is particularly scary.

Based on living 30-odd years in London, most of it using the Piccadilly line on my daily commute and to get to LHR.

Sounding like a TfL groupie here, but it is a pretty good transit system, given geographic and budgetary constraints.