The Director character was originally voiced by Scottish CGI animator for the series Chris Clark. When the quality of his recordings was deemed unusable director Brendan Sheppard stepped in to replace him.
As Rex Duis was providing all the Cybermen voices, he had recorded the Director's lines for his reveal in Part 3 as the Cyber-Director with a slight Scottish accent to fit in with Chris's recording and was unaware that Brendan had used an English accent for the character.
The decision to play Dr. Cavil as Scottish was also made to fit in around the Director's original accent.