I ran the out&back starting from the northern end in Deptford, splitting 42:41 for the upstream and 40:37 for the downstream, making the downstream leg also the new one-way FKT (see picture of rolling split time at the southern end). The upstream leg was slower as it is slightly net uphill, but I was also hampered by a bit of headwind and a navigational error in Ladywell Fields (costing me maybe 30-45”). Since the end points are slightly ambiguous, for the avoidance of doubt: I ran from the bollards on Copperas St / Creek Rd to the barrier at the Kings Hall Rd entrance to Cator Park and back again. This run was solo & unsupported, consuming a couple of gels along the way.
I had jogged most of this route last year - while it is entirely paved and features a few busy road crossings (be careful!), it is in parts a nice path along the local Rivers Pool and Ravensbourne and you get to run the borough of Lewisham end to end (with a bit of Greenwich and Bromley thrown in). I found it nicest last year just after it had heavily rained when you run along to the sound of the water flowing. If you do run it, it’s worth studying the map and taking a gps - the circular metal plates in the pavement and the small WW symbols (second W reflected upside down) on signposts are easy to miss.
These times (both one-way and out & back) can undoubtedly be improved further - I could probably chop two or three more minutes off this with less wind, a little more luck with road crossings, more appropriate shoes (road racers would work best) and fresher legs than I had, and a better runner (especially a local knowing the route well) can undoubtedly improve this further by a significant amount.