Sparrowhawk, nuthatches and possibly a lesser spotted woodpecker

This morning on Tooting Bec Common I saw the Sparrowhawk looking unlummoxed by the Corvid bullying from Friday, parakeets and pigeons screamed as he approached, it's the best way to describe the terrified sound I heard as he flew down from a higher branch, I got a good view of a very pale Underwing and chest, on my home,  near the lido I'm very convinced I saw a lesser spotted woodpecker among the nuthatches , unless it was a very little great spotted, but I was struck by the striped tail, I think it was a male as it had a red head, very small and dainty compared to the great spotted I also saw.