A good question.
A local answer.

Keep a casual takeaway or picnic option nearby if the child is too tired for a long meal.

Confirm the venue's hours and whether the historic interior is actually open to customers.

Compare current Sunday trading, food-stall range and travel time from the gardens for the exact date.

Check the current menu, prices and booking policy directly, especially if a particular dish or waterfront table matters.

Mention the occasion when booking, but confirm any cake or celebration policy rather than assuming it is included.

Keep one quick breakfast option for an early start and one sit-down dinner option for a slower evening.

Check current menus for mains, drinks and any weekend surcharge so the total matches your budget.

Check the actual table view, child-friendly choices and booking time; a restaurant's river address does not guarantee every seat faces the water.

Pick accommodation and transport around the dinner if you want a relaxed evening without a long trip home.

Choose a few dining areas near where you stay and review current menus rather than relying on a single dated restaurant name.

Explore a food market or neighbourhood dining street and compare current menus before choosing a place.

Check restaurant kitchens near your hotel for that Sunday and reserve a realistic arrival time after airport transfer.