Hi,
Lets go with Thursday 30th December and the City of London.
It looks like the train services from Orpington are viable, you'll need to change at London bridge. Here's the details of the Engineering work:
Christmas Engineering worksThe Docklands Light Railway is closed over the holiday period on the Western end (Tower Gateway/Bank) so will travel via Cannon Street using regular trains.
A few suggestions of places to visit would be appreciated. Anything from this guide of interest?
https://mylondonwalks.com/walks/city-of-london-walk-1/Happy to discuss ideas.