There is a page with 201 info, it is written by a guy who has gathered a lot of info on old sewing machines and has worked with the for years. He has most details on the Kilbowie factory. I don't know where he found the information. From a quick search on serial number lits, the earliest UK production I could find was 1934. This is from
his 201 page;
The Singer model 201 first hit the streets just before the Great depression of 1929 but sales really took off for the Singer 201 just before World War II and boy what a machine it was, quite possibly the finest straight stitch domestic sewing machine in the world at the time (arguably it still is). However by 1939 Singer was busy with the war effort and so all but essential sewing machines took a back burner.