Assuming that Arthur Taylor was born in 1880 as you say, checking Freebmd for births registered for Arthur Taylors in 1880, there are well over 100-150. So how ever to find out which is yours?
Generally, with less common names, we would go to the 1881 census to see if we can locate the correct Arthur Taylor as a 1 year old, using various things such as parent's names, place of birth, father's occupation, siblings, etc ... However with your Arthur Taylor we have absolutely nothing to identify him apart from an exact date of birth., and there are hundreds of Arthur Taylors.
To me, it is strange that you know his exact date of birth but not his place of birth.
Do you have any certificates at all for any of these Taylors?
