Canada is the only significant part of the old Empire that stuck with the UK after The Big One in 1947, largely because the only other real option was to be absorbed by the US. This turned out quite well for both Canada and the UK. There is no formal agreement or alliance between the two but they act closely together in the certain knowledge that if they separate, Canada will become part of America and the UK will be absorbed by Europe. In the final analysis, Canada and the UK are defined by negatives. They are not European, not American.
Canada and the UK have a rather greater political impact that Europe (they could hardly have less). They do actually count for something though and American policy makers listen to what they say. This is a combination of practicality (the US defense system has a large Canadian component) and sentiment (the exploits of the British Resistance have become something of a legend). There is, however, a strong strand of anti-Americanism in UK politics, best exemplified by Lord Halifaxs final papers before he was beheaded on Tower Green.
Both countries are semi-socialist democracies. They run on feel-good policies that mostly bite them at regular intervals.