[dredmorbius]

As others have noted, this is false, both were produced concurrently.

Clarke himself provides additional details of the process, as well as omitted excerpts and scenes, in The Lost Worlds of 2001 (1972):

<https://en.wikipedia.org/wiki/The_Lost_Worlds_of_2001>

<https://archive.org/details/lostworldsof20010000arth>