Currently live in South London. I intend to bash every line in the UK that is possible, and have completed most of it (including NI) except the EMT network and parts of Lancashire/Yorkshire. So the nearest line with a regular service I haven't taken is Kettering to Corby (around 90 miles away).
The nearest line with an irregular service is probably some of the diversionary routes around London, but I don't really know how to record this properly as the tracks and junctions are so complicated. According to PSUL, I probably haven't taken the Cally sleeper east coast diversionary route, which I don't see any point in bashing as it would only ever happen in darkness. Based on a recent thread I also haven't taken Thameslink to StP high level, but I haven't checked whether the route is substantially different from EMT.