What about from the H&C to the Bakerloo at Paddington? It's quite a long walk!
That's not in one station, though!
Waterloo and City at Bank to District Line eastbound at Monument, perhaps? Or to the DLR if the District at Monument doesn't count.
Waterloo Jubilee to anything else is of similar length, though since there are travelators, not so long of a walk.
King's Cross St Pancras Victoria Line to Northern Line, now the secret passage is closed off. There's still one by the Piccadilly Line, though. Plus you can use the lift from the ticket hall.
Green Park Piccadilly to anything.
Charing Cross Bakerloo to Northern is famously long. (they were two different stations).
Warren Street and Euston (CHX branch to anywhere else) are deceptively far, Notting Hill Gate (Central to Circle) can be further than you think if you don't know the secret shortcut, so can Leicester Square (Picc to Northern). As, so it seems, can Baker Street Circle westbound to Bakerloo/Jubilee.
At the moment though, reaching the Central line platforms from the Northern line platforms at TCR is the most awkward one - it requires three trains! Well, two if you go up to High Barnet and wait for it to go back down the Bank branch.