You are not legally able to enter Canada with a recent drunk driving conviction - rehabilitation takes rather longer than instantaneously. Quite a few years before they will even consider it.
However , if you are entering on a UK passport, it's not a question they ask visitors, and they won't have access to UK records - so you will be OK.
If you are entering with a US passport then from what I've heard they will probably know without asking and turn you away. (That is if your conviction was in the US)