does anyone know if I can get to Gospel Oak overground from Honoe Oak Park without using the tube? It looks as if this is the nearest station to the ponds and I thought our bit of the overground (from HOP) would link up somehow -I have tried tfl with no luck (or comprehension on my part)

You could take the Overground to Dalston Junction, walk to Dalston Kingsland and pick up the Overground from there to Gospel Oak. The ELL Overground won't join up with the North London Overground until the extension to Highbury & Islington opens (next year?).

Why do you want to avoid the tube? If it's because it's underground then the Overground won't be any good either as the central section is underground.