Martin Underwood wrote:

So did the old bridge have a straight-line access to the trackbed coming
from the south and the station to the north, or was there a sharp kink in
the track at each end as *appears* to be necessary if it was connected
nowadays? I presume there was not a kink: the original bridge would have
been built inline with the track and the platforms and maybe the new bridge
would have had the deviated kinked route, though track has probably been
slewed since the new bridge became the only one.

The tracks on the orginal, upstream, bridge did not serve Blackfriers,
originally called St. Pauls, station. They bypassed this station,
which was built later, and served Ludgate Hill station, and then
descended to Snow Hill, briefly re-named Holborn Viaduct Low Level,
station, which is just North of the present St. Pauls Thameslink; it
closed in 1916, but traces can still be seen. There was originally a
station on the South bank of the Thames, named Blackfriers Bridge. The
through lines at Blackfriers station, reached by the current bridge,
served only Holborn Viaduct station, until the re-opening of the Snow
Hill line as 'Thameslink'. When this connection was built it did have
a kink in it until it was re-aligned after the demolition of Holborn
Viaduct station.

See this site, for details of the closed stations.
http://www.disused-stations.org.uk . There were three stations between
Elephant & Castle and Blackfriers; Camberwell, Walworth Road and
Borough Road, and an Eastern curve North of Snow hill, towards
Aldersgate Street and Moorgate street. There were also platforms on
the West curve at Loughborough Junction, and on the main line at
Clapham and Wandsworth Rooad. The last passenger service on the old
route was Victoria - Moorgate street, but freight continued until about
1970 ish.