My Grandfather was Alfred Bedson, from Crewe in Cheshire. They moved there from Staffs. I shall try to find out more for you. He died before I was born. However I fear that he may be one generation away from the Alfred mentioned in your message. It may have been his Father. My Father, Douglas Bedson, was born in 1921. I was born in 1952.
I have added another four Bedsons to the world, including three sons. Watch our for the registration on my blue/black Merc "BED5ON"!!