"Tim W" wrote

I don't know if it counts, but there is a spur line from London Charing
Cross to London Cannon Street direct.

I think there may be one service in the middle of the night?
(confirmation?)

No, hasn't been a regular service for years[1]. Many years ago the only
timetabled train to use it was the 0053 Charing Cross to Dartford via Cannon
Street (though if you go back to SE&CR days a high proportion of Charing
Cross trains went via Cannon Street). Even further back there was a shuttle
service between Charing Cross and Cannon Street, but this lost its
usefulness when the Metropolitan District railway reached the City. The
shuttle service also lost some of its business when an intermediate station
(Blackfriars Road, later superseded by Waterloo Junction) was opened. Before
then certain 'ladies' used a First Class compartment with the blinds down
for their 'business'.

[1] still gets used occasionally for a Charing Cross - Cannon Street shuttle
service at weekends, if the direct route from Charing Cross to London Bridge
is blocked by engineering work. However, the Thameslink plans show the
Cannon Street connection at Metropolian Junction being severed.

Peter