I have seen Singers that were made in 1950 that are Centennially marked so they could have stock on hand for early 1951. Perhaps those made in 51 that are not badged as a Centennial were made late in the year for the next years market. I really don't know.
I have some of the Canadian made parts in my machines too. Not sure why they intermixed the nations of manufacture but it happens. The motors I understand. UK uses 220 or 240 Volt motors, ( not sure which ) so they just sent the machines over and the country of destination supplied the motor.
Joe