I’m afraid as with many funny Christmas stories and anecdotes this story is not true. Indeed a couple of recent articles debunk this story as untrue and just a popular story.
The Oxford English Dictionary lists it in an article on variations on the word Christmas and its uses. You can find that here: https://public.oed.com/blog/have-yourself-a-merry-little-update/
Further the UK Catholic Herald also has an article which debunks it by exploring all possible origins for it. You can find that here: https://catholicherald.co.uk/comment-features3/
But probably the most definitive way to debunk this is to search Hansard, the UK Parliament’s record of every MP, Lord, debate, committee, question or written answer given in Parliament. They have digitised huge amounts of their records and many of these go back 200 years.
They certainly can tell you if an MP called Thomas Massey-Massey, or an MP with that surname ever existed and I’m afraid he did not.
You can search Hansard here: https://hansard.parliament.uk/
The two articles above give possible origins for the story but whatever it’s origin, it’s certainly apocryphal not least because it appears no MP of that name has ever sat in the House.