In message , David of Broadway
writes

If there is/was a passageway under the road outside the station, how
much more work could it be to connect it inside the station?

An awful lot. The north end emerged in the street not particularly close
to the H&C station. But the real problem would have been on the south
side - projecting the subway any further south would have meant crossing
the District and Piccadilly lines on the level (!) especially to reach
the westbound platforms.

Since the H&C is a surface level station, and the ticket barriers of the
D&P station are also at surface level, a surface-level crossing makes
sense - and I suspect that the solution of a pedestrian crossing also
appealed as a "traffic calming" measure (the subway was never LU
property, so I doubt they had much say in the matter).

--
Paul Terry