Hey, that’s my line! 
It’s a very House of Lords thing to do. He screwed up and missed the session he was supposed to be at. But an apology would have been seen as insufficient, so by offering to resign even though he knew the resignation wouldn’t be accepted he was signalling that he accepted that he had screwed up, while also opening himself up to the sort of gentle chastisement of his peers for his grandiose gesture that serves as an actual proportionate punishment for his mistake. The wording of the Downing Street response (I mean, the phrase “with typical sincerity” is drily hilarious) supports this interpretation.
Ironically, if the PM had accepted the resignation, *she *would have been seen to be overreacting to the incident.