I have been trying to verify an external email account so that I can
use gmail to retrieve my email at the office.

I get to the part where email is sent with the verification to my
office account.  I receive the email at the office with the
verification number (5 digit number) & I enter that number in the
verification box as directed or I click on the supplied link (i've
done bot and the verification fails.

The server at the office is running Sendmail 8.11.0.

I have no trouble logging into  pop3 at the server.

forward the verification email back to your Gmail address, and click
on the verification link at home, maybe it is only the work server
that blocks it.