The Honor Oak (St Germains Road) is I think open 12pm/6pm and along Brockely Rise the Brockley Jack 12 to 3pm for drinks; the General Napier may be open too.

The Greyhound at Sydenham Kirkdale is open 12 to 6pm. They are doing Christmas Day menu, so whether opening includes drink only not sure.

For a Spoons experience, the Moon and Stars at Penge is open.

I would check with the pub though before heading out - some may be booking only.