When Kelly suggests they steal the 'Girl With a Pearl Earring' portrait, the Posh Totty group reply "Oh my god, you want us to steal Scarlett Johansson?", referring to the film Girl with a Pearl Earring (2003). Colin Firth, who plays Geoffrey Thwaites in this movie, played the painter in the film with Johansson.
The picture in Miss Fritton's study is a painting of Alastair Sim, as he played the original role in the original films. The bust that is destroyed by Annabelle's hockey blow also has the features of Sim.
When the girls first get off the bus and stampede through Trafalgar Square, we can see members of the public are being held back behind railings to keep them out of the girls path. They're also very obviously watching filming.
When the teacher gets off the Cheltenham Ladies' College coach and talks with the minister, she says: "Between you and I..." No real CLC teacher would have perpetrated that glaring grammatical mistake.