This is the Swaledale (Yorkshire Dales) method of counting sheep,as I learnt it:

Yan, Tan, Tether, Mether, Pip, Azer, Sezar, Akker, Conter, Dick Yanadick, Tanadick, Tetheradick, Metheradick, Bumfit, Yanabum, Tanabum, Tetherabum, Metherabum, Jigget.

The count doesn't go beyond 20, because a stone was dropped for every group of 20 sheep counted,and if there were more sheep the count started again.

I don't know of a Welsh version for counting sheep specifically, but one to ten in Welsh is: un, dau, tri, pedwar, pump (pron. pimp), chwerch, saith, wyth, naw, deg, which has similarities.

My own theory is that it originated with the Brythonic speakers and spread down from the North of England as the Brigantes tribes pushed downwards. Tacitus seems to suggest that by the time the Romans invaded just about the whole of what we now know as England was populated by people of Celtic blood.