Question: Can I exit and then reenter Canada on a tourist visa immediately after having a student visa?
After doing some quick research it seems as if your plan to return to England and then going back to Canada on your English passport as a tourist would be a fool proof way of getting back into the country after your student visa expires.
But it seems as if you have many other options for re-entering Canada:
As a rule of thumb, as you are a duel passport holder (Australian and UK) I do believe that you could also re-enter on your Australian passport as well without difficulty. It does not seem as if Canada or the USA (the two countries sort of act a little in tandem when it comes to immigration) has a set amount of time that you need to be outside of the region before returning for another entry on the visa waiver program — you just need to exit Canada, the USA, Mexico, and the Bahamas before returning. Though keep in mind that re-entry is always left up to the discretion of the immigration official.
Though I do believe that returning to the UK and then returning to Canada on your British passport would be your best course of action. It seems as if you can get 90 days upon entry which could possibly be extended while in Canada.
Or, you could go to England and apply for a six month tourist visa to Canada.
Or, if you are under 33 years old, there is a 3 to 12 month working holiday visa to Canada that you could apply for.
Or, perhaps you could request a tourist visa at the expiry of you student visa while in Canada and not need to do a visa run at all. I am unsure if this is possible, but it may be worth heading to an immigration office to inquire.
So there seems to be a few options for returning to Canada after the expiry of your student visa. Your original plan of going to England and returning with your UK passport seems best, but other options could work as well.
Canada seems to have somewhat open immigration policies in regards to UK an Australian citizens, it does not seem as if you should have much trouble getting a tourist visa at the end of your term as a student.
Original question about traveling to Canada after expired student visa
I hold dual passports, Australian/Uk. I am currently in Canada on a study visa which runs out in 2 months. If I cannot get an extention what is there to stop me from flying back to the Uk and returning on a visitor visa using my Uk passport. Do they have a way of cross referencing passports at the immigration?