"...family lore is that she was a London socialite" -- Yes, because a London socialite would choose a life of grinding poverty with an Irish coachman ... for love. Outside Catherine Cookson novels this doesn't happen.
I've searched UK records for a suitable marriage and drawn a complete blank. FreeReg's coverage is very patchy and the lack of a suitable birth doesn't mean much.
I did find one glimmer of interest in the 1841 census. Unfortunately this census didn't contain very much information but I did find a John Flanagan and an Emma Dawson in the same district. Emma is a servant in the household of Lord Kilmaine. There are many Irish-born servants in the household and she could've known John through them.
"England and Wales Census, 1841," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MQJK-CHF : 22 May 2019), Emma Dawson in household of Kilmanie, Lord, St George Hanover Square, Middlesex, England, United Kingdom; from "1841 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives, Kew, Surrey
John is literally round the corner. It's not clear to me what this residence was - possibly a lodging house. I subscribe to FindMyPast so can see the images but they don't add much. He's described as a S... M - possibly a stable man. There are a few others with the same designation on the page.
"England and Wales Census, 1841," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MQJZ-53V : 22 May 2019), John Flanagan in household of George Hikey, St George Hanover Square, Middlesex, England, United Kingdom; from "1841 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives, Kew, Surrey