I've done this before when I was getting my UK passport renewed and had to travel to Canada (where I was born). I showed my Canadian passport, they asked my purpose of travel, etc. I said I was actually a UK citizen who lived in the UK but my passport was being renewed. I'd taken a photocopy of the expired passport to bring along just in case and they did ask for that. A bit of typing and all was well. No stamp in my Canadian passport.