Septimus is my great-grandfather. This is the information I have so far:
Born in Westoe, Durham 1857/8. I am confident that Septimus is the same person as Arthur Septimus Thompson mentioned in some resources.
1861 census (taken in South Shields) shows: father William Thomas Thompson, mother Margaret, siblings M.A. Thompson (aged 14), Jane (aged 13), F.H. Thompson (aged 11) Edward (aged 4), Matthew (aged 4), Septimus (aged 1).
1871 census (taken in South Shields) shows: Margaret Thompson (aged 55, retired farmer), Robert (aged 27, a timber merchant's clerk), Foster Hewison (aged 21, an engine fitter at Works), Edward (aged 19, a pupil teacher), Matthew (aged 14, a clerk at Chemical Works), Septimus (aged 11, scholar).
1881 census (taken in South Shields) shows: Margaret Thompson (aged 64), Edward (aged 29, labourer at Glass Works), Septimus (aged 21, butcher), Isabella (daughter-in-law, aged 26), Robert (grandson, aged 5), John (grandson, aged 3)' William (grandson, aged 1).
1883 South Shields register records Septimus as a butcher (address 40 Dale Street).
I have a suspicion that Septimus migrated to Melbourne, Australia, arriving from London on the Clyde in May 1887. Needs further research.
Marriage certificate: 16 January 1889 Married Rosa Marie Grimsley in Melbourne, Australia. Marriage at Church of England, Moor Street, Fitzroy. Daughter Hilda Margaret Thompson born later that year.
21 June 1897 Septimus's cause of death on certificate listed as phthisis (tuberculosis). 
Circa 1902 Rosa remarried Wilfred/William/Willie Wraith and has two children - William and Florence.
Puzzle: The marriage and death certificates record that Septimus was a butcher, and all of the background details match. Death certificate shows he was single and aged 40 when he died. The marriage certificate gives his age as 27, which should have made him 35 at time of death. I've searched the divorce records for the time and there is no record of Septimus and Rosa divorcing. The best guess I can come up with is that they separated some time before he died and he regarded himself as single.
If anyone has any information about Septimus's immigration to Australia or any other family details I'd really appreciate it.
Peter