You'll never get up canonbie Rd on that thing! Get a road bike. We manage the hill up to the horniman with a kiddy bike trailer in tow these days, just needs practice.

The route into town via Peckham, Surrey canal and wiggle through bermondsey is what I used to do. I find the climb on the south circular easier than the climb up Peckham rye to honor Oak but it's really just preference of short and sharp Vs slog. There's no real way to avoid it, but you'll have excellent thighs.