V'ger is not the precursor to The Borg. Roddenberry didn't create The Borg.
Now The Cybermen as the precursor to the Borg. Yeah.
As a matter of fact I'm not sure how Star Trek was never sued by the BBC for the copyright infringement. The Borg and the Cybermen are too close!
The idea of cybernetic beings did not originate with Doctor Who
. You can actually trace their earliest (known) appearances in science-fiction stories as far back as the late 19th-Century.