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I'm staying with my parents in Sanderstead at the moment and have been riding round here on and off for probably 30 years. Chelsham etc is good for CX/gravel IME and there are plenty of tracks criss-crossing if you take random turns and explore. I don't have strava so can't share I'm afraid.
Addington Hills, Croham Hurst and Spring Park are all good in winter apart from the crowds during the day. Gravelly soil drains really well compared to the chalky clay further out!
14psi for Croydon's finest gnar last night. Mud spikes aren't great for hard snow...