Okay so this what we did in the end. We started in Sutton to avoid getting drained of energy in an attempt to just get out the megalopolis. Sutton is at the southern edge of the capital and we went there by train from Victoria Station. From there, we cycled on mostly B roads but also on some A roads, some more dreadful than others but nothing too life-threatening but annoying and noisy. We camped outside of Petersfield. The following day, my mate complained that it was too hilly and hot so he threw in the towel and took a train back to London from Eastleigh. From there on, I continued alone and cycled across the northern part of Southampton and soon I found a cycling path leading straight into the New Forest, a glorious place! As trains were not working and rail replacement buses were not taking bikes, it was too much of a hassle to return to London that evening so I ended up staying another night, this time, at a very cozy camp site ran by the Forestry Commission in Ashurst. The following day, I spent the whole day cycling around the New Forest, mostly on forest tracks and in the evening, I cycled to Southampton Airport Parkway train station, the closest point from which to get on a train back to London (Waterloo). I did 160 miles in three days.