Update (October 2012): Sadly the pub has now been demolished. But I think a better candidate for the eponymous Osborne is Francis Osborne, 1st Baron Godolphin, MP for Cambridgeshire 1810 to 1830. The blazon for him is:
Arms: Quaraterly, first and fourth, quarterly erm. and az. a cross or, for Osborne; second and third, gu. and eagle with two heads displ. betw. three fleurs-de-lis, two and one, ar. for Godolphin
Crests: Frist, an heraldic tiger, statant or, tufted sa. for Osborne; second a dolphin embowed sa. for Godolphin.
Supporters: Two eagles reguard. wings displ. and inverted ar.
Motto: Pax in bello
Encyclopaedia of Heraldry, or, General Armory of England, Scotland and Ireland, John Burke, 1844.