There is a John Harrington in Fulham, in 1841 with older (50) Mary H, probably mum, and children Patrick (1), and Mary (7). There's also in 1841 in Whitechapel a John Harrington (35) b 1806 Ireland, labourer, with Ellen also 35 and born Ireland, are either of those any use?
Possibly sibling hunts may help?
Think Mary Modem may be same as Mary Harrington from ages.