Catch a West End musical or play in Soho/Theatreland — book in advance where possible; shows are a great solo evening activity (check exact start time and book tickets).
Pleasant riverside and park walk to Buckingham Palace; on some Sundays the Changing of the Guard happens — confirm the official schedule before you go.
Take photos and learn the history of Britain's political heart; Westminster Abbey may have restricted visiting hours on Sundays so plan for exterior views.
Popular riverside restaurant with great views of Tower Bridge and relaxed seating — book a table (or the igloo in winter) for a comfortable solo dinner.