There are two lineages of J-M241>Z1043 descending from a man who lived 600 BC (YFull estimate) with mutation BY38004 that are now found living in Scotland and elsewhere in the British Isles.
One of these men went on to sire S18238 around 13 generations ago, estimated from GD 5/67. This could be anywhere from 300-700 years ago.
Many S18328 are living in Scotland and one is from East Lothia. His surname became established in Lanarkshire, Scotland in the 13th Century but may have originated in Northumberland or Leicester. In the Iron Age East Lothia was home to the earliest known capital of the Votadini, described as a Brythonic Celtic culture (meaning coming from Britain as opposed to Ireland).
Another S18328 traces to an ancestor born in County Down, Ireland in 1790. His surname is of medieval Scottish origin and derived from northern Old English for "roe deer". His closest matches with the same surname are from Scotland and his most recent common ancestor with the East Lothian lived approximately 9 generations ago, calculated from GD 3/67. This could be from 200-400 years ago.
So the simplest explanation is that S18328 is of Scottish origin and the presence of one descendant in Ireland by 1790 could have been the result of the Plantations of Ireland.
All living BY38004(xS18328) of the British Isles may descend from one man who lived about 31 generations ago, computed from GD 13/67. This could be about 800-1200 years ago.
Most of this group have not provided me their genealogical origins to the Old World. They are organized into two sublineages.
The first group is comprised of three men whose ancestor lived about 19 generations ago, computed from GD 7/67. This could be 400-800 years ago. One is from England and has a surname that is an anglicization of the Gaelic word for "dark". Another has a surname found frequently in Ayrshire that is an anglicization of Scottish Gaelic for "son of the harpist or fiddler". A third has an Old English surname pertaining to bridges.
The second group is comprised of men whose ancestor lived 23 generations ago, computed from GD 9/67. This could have been 600-1000 years ago. One of the men coincidentally has the same surname as the East Lothian. The other has an occupational name that cannot easily be traced.
So it seems that S18328 and the British BY38004(xS18328) both appear to originate in Scotland or England.
So far the only other BY38004 is a man tracing his origin to Omoljica, Serbia with a surname indicating Swiss origin.
By far the simplest explanation for the presence of two child lineages in the British Isles is that BY38004 himself migrated there during his lifetime around 600 BC and sired the two lineages which later diversified.
It is known from archaeology that there were extensive trade links across the English Channel during the Iron Age, which facilitated the diffusion of Hallstatt and La Tene culture. Perhaps BY38004 represents a vector of this migration.
Another possibility is that two child lineages of the BY38004 man migrated to Scotland together at the same time as allies.
While it cannot be ruled out that both lineages independently migrated to Scotland sometime after 600 BC, this is not the simplest explanation. To me we would be going out on a limb to assume that hundreds of years after being descended from an ancestor on the continent, the two lineages happen to both independently move to Scotland and are not found anywhere else.