I'm no good at early rising (and can't ride mid-week) but most parks have seemed pretty full. BPP has some
good bits and thankfully the walkers avoid the muddiest trails. Any of the paths through the woods aren't really any fun with the level of people there at the moment, I can't be blasting through peds like the good old days.
Blackheath dips is also quite fun if you're passing through.
Every time I ride through Greenwich park I imagine a WC level cross race with the course ploughing up and down that huge hill :(