I don't disagree, but I'm not sure the statement about step free access was accurate, particularly at the key interchanges which are relevant to the posts.
I stand by the statement that it is poor and that many key interchanges still lack step free access.
For London mainline terminals (i'm including london bridge because while it's not physically a terminus station, a lot of trains into london do terminate there).
Euston - no step free access from the mainline to the Deep tube, step free access in the westbound direction only on the subsurface lines
Kings Cross/St Pancras - full step free access.
Liverpool street - no step free access to the deep tube, step free access in the easttbound direction only on the subsurface lines
Fenchurch Street - nearest undergound station is tower hill which does appear to have full step free access.
London Bridge - Apparently has step free access to all platforms, BUT you have to use specific entrances depending on your direction of travel.
Cannon Street - Step free access westbound only.
Charing Cross - No step free access.
Waterloo - Step free access to the Jubilee line only
Victoria - Full step free access.
Paddington - No step free access to deep tube, limited step free access to subsurface lines.
So out of the 11 London terminals, 3 have full step free access to all the underground lines serving them (two of which share the same underground station), one has no step free access to the undergronud at all, one has step free access to all lines but you may have to use a specific entrance depending on your direction of travel, one doesn;t have an underground station of it's own but the nearest underground station does have step free acccess and the remaining 5 have step free access but only to a limited selection of lines or directions.
Ok so what about interchanges between underground lines.
Bakerloo/Central - no step free interchange.
Bakerloo/Circle - no step free interchange.
Bakerloo/District - no step free interchange.
Bakerloo/Hammersmith and City - no step free interchange.
Bakerloo/Jubilee - step free interchange northbound to northbound and southbound to southbound possible at baker street but not northbound to southbound.
Bakerloo/Metropolitan - no step free interchange
Bakerloo/Northern - no step free interchange
Bakerloo/Piccadilly - step free interchange northbound to northbound and southbound to southbound possible at oxford circus but not northbound to southbound.
Bakerloo/Victoria - no step free interchange
Bakerloo/Waterloo & City - no step free interchange
Central/Circle - no step free interchange.
Central/District - step free interchange, but only outside the city center at Ealing Broadway or Mile end.
Central/Hammersmith and City - step free interchange, but only outside the city center at Mile end.
Central/Jubilee - step free interchange at bond street.
Central/Metropolitan - no step free interchange
Central/Northern - step free interchange to the Charing cross branch at TottenhamCourt Road, but not the Bank branch.
Central/Piccadilly - no step free interchange
Central/Victoria - no step free interchange
Central/Waterloo & City - no step free interchange
Circle/District - lots of options for step free interchange
Circle/Hammersmith and City - lots of options for step free interchange
Circle/Jubilee - step free interchange on the south side at Westminster, but not on the north side.
Circle/Metropolitan - lots of options for step free interchange
Circle/Northern - step free interchange on the north side of the city to the Bank branch at Kings cross st Pancras, but not to the Charing cross branch.
Circle/Piccadilly - step free interchange on the north side of the city only at Kings cross st Pancras.
Circle/Victoria - step free interchange on both the north and south sides of the city at Victoria and Kings cross St pancras.
Circle/Waterloo & City - no step free interchange
District/Hammersmith and City - westbound to westbound and eastbound to eastbound only at Aldgate east. Step free interchange but requires switching stations at Hammersmith. Full step free interchange at Edgeware road.
District/Jubilee - Full step free interchange at Westminster
District/Metropolitan - No direct interchange (step free or otherwise)
District/Northern - no step free interchange.
District/Piccadilly - no step free interchange.
District/Victoria - step free interchange at Victoria.
District/Waterloo & City - no step free interchange
Hammersmith and City/Jubilee - no step free interchange
Hammersmith and City/Metropolitan - lots of options for step free interchange
Hammersmith and City/Northern - step free interchange to the Bank branch at Kings cross st Pancras, but not to the Charing cross branch.
Hammersmith and City/Piccadilly - step free interchange at Kings cross st Pancras.
Hammersmith and City/Victoria - step free interchange at Kings cross St pancras.
Hammersmith and City/Waterloo & City - No direct interchange (step free or otherwise)
Jubilee/Metropolitan - step free interchange at Finchley road (or Wembly park with some Caveats about traveling in the correct carriage)
Jubilee/Northern - No step free access to the Charing cross branch. For the bank branch London bridge has step free access, but has a warning about having to use the correct entrance depending on direction of travel, so it's not clear to me if you would have to leave and re-enter the station.
Jubilee/Piccadilly - step free interchange at Green park
Jubilee/Victoria - step free interchange at Green park
Jubilee/Waterloo & City - no step free interchange.
Metropolitan/Northern - step free interchange to the Bank branch at Kings cross st Pancras, but not to the Charing cross branch.
Metropolitan/Piccadilly - step free interchange at Kings cross st Pancras.
Metropolitan/Victoria - step free interchange at Kings cross St pancras.
Metropolitan/Waterloo & City - No direct interchange (step free or otherwise)
Northern/Piccadilly - step free interchange at Kings Cross St pancras to the bank branch, no step free interchange to the charing cross branch.
Northern/Victoria - step free interchange at Kings Cross St pancras to the bank branch, no step free interchange in the north to the charing cross branch. Interchange in the south at stockwell northbound to northbound and southbound to southbound only.
Northern/Waterloo & City - no step free interchange
Piccadilly/Victoria - step free interchange at Kings Cross St pancras or Green park.
Piccadilly/Waterloo & City - no direct interchange (step free or otherwise)
Victoria/Waterloo & City - no direct interchange (step free or otherwise)
I count.
5 line pairs with no direct interchange at all
20 line paris with interchange for people who can climb steps no step free interchange
13 line pairs with step free interchange with caveats, such as being outside the city center, only in some directions or only serving some branches.
17 line pairs with proper step free interchange
That is umm better than I expected but still poor.