First proposed in 1848, the gestation of the NT is complex (see the NT's own site). The first site for the NT was acquired in 1913, immediately behind the British Museum, at the corner of Gower Street and Keppel Street. Here a “Shakespeare Hut” was used for entertaining the troops in WW1 but the site was sold in 1922 and the London School of Hygiene and Tropical Medicine was built there. Various other sites were considered and then in 1938 another site was purchased, Cromwell Gardens, opposite the Victoria and Albert Museum. In 1942 the LCC exchanged this site with one on the South Bank, to the west of Waterloo Bridge, and Sir Edwin Lutyens and Mr Masey designed a building. The 1951 foundation stone was laid at this site but a year later it was agreed with the LCC that the theatre should be further west, next to County Hall.
Denys Lasdun was selected as the architect. Meanwhile theatrical productions were put on at the Old Vic and on 22 October 1963 the newly formed "National Theatre Company" opened its first play, Hamlet. Thus there were celebrations in 2013 for the 50th anniversary of the company, even though the building came much later.
In 1967 the site was moved for the last time to the current site (obviously). Building began but it was much delayed and the 1976 foundation stone was laid when only the Lyttelton and Olivier stages were operating. The Cottesloe opened in March 1977. The 1988 plaque commemorates the renaming to the "Royal" National Theatre marking the 25th anniversary of the company's first performance.
In the 1990s millions were spent renovating the building. At that time Lasdun's style was out of favour and the changes introduced caused Lasdun to demand his name be removed from the 1976 stone (we can see that his wishes were not acted upon).