Museums are free; the "attractions" are not

The national museums are free to enter: the British Museum, the National Gallery, Tate Modern, the V&A, the Natural History Museum, and the National Museum of Scotland in Edinburgh. The heavily advertised paid attractions (the London Eye, the Dungeon, Madame Tussauds) cost a lot and line up long. If you do want the view, booking online in advance is cheaper than the gate, and St Paul's dome or the free Sky Garden (reserve a slot) give a comparable one.