V&A South Kensington
Design, objects and small details worth a second look. The permanent collection is free; ticketed exhibitions have their own admission.
Notes from the cityLondon
A free collection, a ticketed exhibition and a market with no entry fee are different kinds of outing. Plan for the one you actually want.

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Start with the experience, then look at the price. Walking into a museum does not necessarily admit you to every exhibition inside it. Entering a market does not include lunch. A free park can contain activities with their own charges.
The National Gallery and V&A both offer free general admission alongside separately ticketed exhibitions. Borough Market is free to enter, while anything you buy is its own decision. The Royal Parks are free to explore, with individual facilities and activities priced separately.
That distinction leaves plenty of room for a good day on a small budget. Choose the free part deliberately, check opening times and keep optional spending optional. Use the linked place pages and official sources for the latest checked details.
Design, objects and small details worth a second look. The permanent collection is free; ticketed exhibitions have their own admission.
A free collection on Trafalgar Square. Choose a handful of paintings and give them the time a whole museum sometimes steals.
A place to browse, buy ingredients or build lunch one decision at a time. Entry is free; the food is a separate budget.
An unhurried patch of London: gardens, open space and a walk that does not need a destination. Ordinary park entry is free.