Public consultation took place in early 2019 on Westminster's proposals for the Strand/Aldwych area.
The main proposals were to change the north side of Aldwych gyratory system into a four-lane, two-way road, and remove all motor traffic from its south side (Strand) except for a few local connections. See plan below.
(Click image to enlarge.)
The plans showed no formal cycle route through the south side of Aldwych, and no way for eastbound cyclists to enter at the west end and exit and the east end.
The supplementary information on the webpage https://strandaldwych.org/news/strand-aldwych-cycle-routes/ was helpful; but although it said there would be shared-use footways, pedestrian & cycle zones and Toucan crossings, these were not shown on the drawings.
The Aldwych is typical of the gyratory systems of the 1960s that are now largely discredited and a hostile environment for cyclists: at some point you will probably have to cross at least two lanes of fast-moving traffic. Not to mention the noise, fumes etc. Not much fun for pedestrians either!