David, Posting this again for the back burner and info. Following the post by MonicaL and yourself re the "F" in name. If, and I mean if, he was Thomas Francis McDonough then he may well have been economical with his info. There is a birth of a Thomas Francis in 1904 Birkenhead with mmn Mason. His parents marriage 1903 Birkenhead--William George McDonough & Agatha Mary Mason. Agatha & children in 1911 census below.
https://www.familysearch.org/ark:/61903/1:1:XW3J-BBTOne of the residents in the house is a Daniel McDonough aged 57 (C1854) married. Could this possibly be the Daniel who married Mary Gerrard on the 23.7.1882 who was aged 27 (c1855) at marriage.
Changing the subject, was the Jeanie Muir McFall the daughter of John & Elizabeth the one you were looking for, if so a great result.
John