I've got a couple of routes that I like to take - but need to expand the range since I'm aiming to do a half-marathon in October.

I really enjoy running down to Dulwich Park and round the loop there. There are lots of runners, cyclists and roller-bladers so it always feels pretty safe and there are so many trees that it can be shaded - and there's an option to 'trail' run around the perimeter or take the road options. It's just over a mile around the road route and most people seem to do a few laps. It does have the benefit of being relatively flat although there are a few gradients to help with picking up the pace.

Peckham Rye is also a good place to run around/through. I've got one 10k route that takes me along Wood Vale, down round Peckham Rye, back up Barry Road, along Lordship Lane, down Court Lane and then a couple of times round Dulwich Park.

I'd like to run in the woods (despite the initial hill up to them from Harvester) but not entirely sure how safe I'd feel since they can seem quite empty at times.