Jerome's flat is a great place to say if you're a single traveller and you already have some experience getting around London. The bedroom is clean, well-lighted and spacious. There is also a fold-out bed for a second guest, but it's not really a space for couples. Despite being just off a main road, the flat is incredibly quiet day and night.
In terms of location, Peckham is not on the Tube map. It's extremely well served for buses, though, and Jerome's flat is a fifteen-minute walk from Peckham Rye station, where you can get trains to London Bridge (10 minutes) and London Victoria (25 minutes). It also has regular Overground services to East London. A certain prior knowledge of London will really help you get around, and Peckham itself is full of good places to eat and drink.
Jerome is a lovely respectful man, who was in touch regularly to make sure everything was going all right.
The flat is only accessible by stairs, so if you have any mobility restrictions I couldn't recommend it, but for anyone else who needs a quiet place to stay for a few nights, it's a winner.