- You may be looking for International Gallery.
The National Gallery was an art museum on Trafalgar Square in London. The museum had a secret annex, the Under Gallery, which was constructed by Elizabeth I to house any art deemed too dangerous for public consumption. Gallifrey Falls No More was among its collection. (TV: The Day of the Doctor)
When the Twelfth Doctor was trapped in 1972, he visited the National Gallery with Maxwell and Jess Collins. While they looked at The Hay Wain, a small alien ran past them being chased by three alien hounds. The Doctor, Jess, and Maxwell followed the hounds outside into Trafalgar Square. (COMIC: Bloodsport)
In 2013, UNIT brought the Eleventh Doctor and Clara Oswald there to discuss a Zygon breach. It was there that a time fissure brought the Eleventh Doctor to 1562 England to meet his tenth incarnation. After combining forces with all his incarnations to save Gallifrey from its destruction at the conclusion of the Last Great Time War, the Eleventh Doctor met with the museum's curator, who told him of the true meaning behind the painting (TV: The Day of the Doctor)