So for anyone else looking at this thread, here is what I found:
Applied through Lewisham for the max 3 sites as allowed
Blythe Hill - 186 on the waiting list
Hurstbourne Road - 79 on the waiting list
Priestfield Road - 63 on list
I also applied for 2 private allotments in Lewisham.
I then applied for a variety of allotments in Bromley through http://balgf.org/ as well as a couple of in Southwark (Dulwich really).
Most are fairly non-committal on waiting list times \ list other then saying no chance this year (this is not a criticism by the way. I’m sure people have better things to do with their time, like looking after their allotments!).
Anyway, I decided I would apply for any within a 15-20 minutes drive. Most sites were full, but some suggested they may have space next year and some of their waiting lists clear quickly, and better than that I was offered a half-plot on one site within 2 days of applying. Now it’s a small side and the other end of the scale to something like Kent House Leisure Gardens, but I can start and learn tomorrow. I’ve got it on a 1 year trial basis due to the distance, which suits everyone - worse case for the allotment I’ll clear the plot for them (or someone else) and best case I’ll be there for years. I’d ideally like a bigger plot closer to me, so will see if anything else comes up next year once I have some experience under my belt.
Dorset Road which looks amazing I made it to 20 on the waiting list, which I thought was surprisingly low for such an amazing looking site.
Anyway, I guess Lewisham looks diffcult, Bromley if you are prepared (or can) travel a bit seems a better bet for the short-term. The private Lewisham sites may be better but I don’t really know.
Good luck anyone else - hope the above helps a bit!