It looks like most of the Canadian ships used the white ensign so Ubisoft was probably correct in using the same flag for Britain and Canada.
After doing some research I found that most Canadian warships used the white enisgn but I found a few pictures using the red ensign.
Here's the HMCS Algonquin "V" Class Canadian destroyer using the white ensign:
Here's the HMCS Sackville "Flower Class" Canadian corvette using the red ensign:
