Yes. Some undertakers have been professionally trained. They’re the ones with the initials Dip FD after their names. The two trade associations, the National Association of Funeral Directors and the Society of Allied and Independent Funeral Directors, who represent between them most undertakers in Britain, are very keen on training – but they don’t insist on it as a condition of membership.
Should it matter to you? Inasmuch as some of the very best funeral directors do not have a Dip FD, no. They learnt their trade on the job. They served a good old-fashioned apprenticeship, starting by washing cars, driving and pallbearing, and advanced through the ranks. These are practical people and they learn by doing.
The most important attribute of a funeral director is emotional intelligence, and there’s no exam that can test for that.