Earlier quoted context omitted.
I was working my way to it, when IT rolled out a new policy of "cannot share more than 2 consecutive characters with a previous password" or something like it, included in an email along the lines of "an audit has found this new policy applies to you". Dicks.
If that policy is enforceable, someone would have to be storing passwords in plaintext, or the hashing algorithm is too weak. IT shouldn't be able to tell anything about plaintext password similarity beyond equals or not-equals.
But at the time of the password change, no, assuming password changing requires you to enter your current password as well.