I am a dual British/Canadian with a passport from each nation. Can I use the Canadian passport to enter/leave Canada and the British passport to leave/return to the UK?
Yes you can.
Canada has no exit checks. Britain has recently instituted them, but I see no sign that they will require you to exit on a British passport (they don't require you to enter on a British passport). Neither have a problem with you being a dual citizen. And either passport will get you visa-free access to the other country. This question gives you more general advice on using two passports, but in this case it's not a big deal. Show either one whenever. The only place where it makes a difference is coming to Britain, where showing your British passport gets you in the fast immigration line. (Strangely there is no equivalent benefit in Canada).