So, the closest record to an anti irish surname law we have of is the 1429 Tynwald Court restrictions on the residency of Irishmen, Scottishmen and other aliens - and its repeal in 1696 (aside - they must have assumed that the 1690 victory in Ireland would end all unrest - little did they know!).
If this official attitude existed before the religious wars in England, it can only have intensified in the first half of the 16th century - producing enough pressure to encourage the alteration of name forms which were too obviously Irish or Scottish.
Presumably Mac***** names were acceptable again after 1696 and fresh Irish and Scottish immigrants were able to retain their hereditary surnames without hindrance.
Still, I would like to find where I read that a law banning Mc***** names had been passed. True or false, when I rediscover the reference I will let you know.