Leading 0-2 to 0-1 after a tight opening half, the visitors reeled off six points on the spin, before a Lorcan Mulvey penalty in the 64th minute gave London hope.
Flanagan was satisfied his young team survived a tricky assignment: “I expect us to get out of this division. I think Offaly are good enough. We didn’t play particularly good football but I think there is an awful lot more in us.
“We were very nervous coming here. We have got a win in a competitive match and that is a start.”
Scorers for Offaly: B Allen 0-3 (3fs), D Hogan, G Guilfoyle 0-1, P Sullivan, W Mulhall, N Dunne, R Allen 0-1.
Scorers for London: L Mulvey 1-0 (pen), A O’Hara 0-2.
OFFALY: A Mulhall; D Brady, P McConway, J O’Connor; C Donohue, J Maloney, D Hogan; G Guilfoyle, R Allen; E Carroll, P Sullivan, N Bracken; B Allen, N Dunne, W Mulhall. Subs: D Kelly for W Mulhall (53), J Evans for Bracken (53), N Smith for Carroll (55), M Young for Sullivan (60), N Darby for Hogan (63).
LONDON: B Kavanagh; D McCarthy, P Butler, P Galvin; C Og Greene, M Carroll, D McBride; M Gottsche, A Bradley; G Crowley, S Conroy, C Sheridan; A O’Hara, A Moyles, L Mulvey.
Subs: B Smith for Moyles (48), M Walsh for McBride (52), S Curran for Greene (55), S Hickey for Conroy (60).
Referee: G McCormack (Dublin).