Thanks for your response. Margaret's parents being Peter and Janet make it just about certain that Alexander was Robert Irving's grandson, and almost certain that he was the son of William.
Thus six children were named after grandparents and parents (I didn't know before that a Margaret was mother as well as aunt) and Ann and Catherine were aunts.
So this takes your husband's geneology back another two generations to 1732.
My distant cousin Dorothy - named after Alexander's other aunt - discovered all this in the 1970's and went up from Sussex to Carlisle to meet some other descendants. I imagine she tried to go back further and failed so it can't be easy.
Do let me know anything else you discover. I now have a line from Robert Irving in 1732 and the undated parents of a Mary Robson who was born in 1738 down to my latest grandchild born in 2002 and my youngest son born in 1993 - 10 generations on the longest line.