Found out Thomas Mortimer Walters who died in 1844 was 38 yrs old, so born c1806, a fair bet he was Jane's husband. (Also fits with Thomas and Fanny's Thomas b 1806 - I think I will go back to try to find out more about them.)
So I guess Thomas and Jane marry in 1838 in Liverpool, Thomas jnr is born in 1840 in Newcastle upon Tyne, they are in Sheffield in 1841 (maybe), Horatio is born in Chorlton in 1842, and Thomas dies in 1844 in Chorlton. In 1851, Jane is (maybe) a cook in Liverpool, Thomas is with his aunt in Bilston and Horatio is with his uncle in Liverpool. Jane gets married again in 1860 in Liverpool to George Fishley who's a crew man on the Wansfell. Maybe Horatio is at sea in 1861. Can't find any reference to Jane, George (maybe at sea) or Thomas in 1861, but somewhere between 1860 and 1864 Jane, George and Thomas all go to Australia, although probably not together as Thomas seems to be alone on the passenger list for the Wansfell in 1863. Phew! Thank you so much - that's a lot more than I knew a few weeks ago.
I also stumbled across a reference to a Valentin Walters b 1752 in Aylsham - I have no idea how common the name was, but would be about the right age to marry Mary and have those children including Thomas in 1785, although Norfolk is a bit of a way from Middlesex (again geography not my strength).
Thanks again for all your help Rosie!