Should councillors caught drink driving have to resign?

A Conservative councillor in Walsall, Cllr Zahid Ali, has pleaded guilty to drink driving. As a result he may have to resign from the West Midlands Police Authority. The Walsall Advertiser helpfully points out that the Code of Conduct for councillors includes a requirement that "Members should uphold the law." So should he resign as a councillor? What if he had broken the law by breaking the speed limit rather than drink driving? How many councillors would be left if that creiteria was applied?