Flixton Hall, where most of this is filmed, had been considered by the future Edward VII for his country house, but eventually he chose Sandringham House as it had better rail links to London. It was home to the Adair family for many years but was sold to a property developer in 1950 to pay Death Duties. The new owner stripped the roof of the valuable (and protective) lead covering, clearly seen as the boys run across it, and allowed the structure to decay until he could get permission to demolish it in 1953. Elements of the ground floor are all that remain, and are used to store farm machinery. The grounds are noted for a giant Sequoia.
The Rembrandt appears to be 'Girl at a Window' (1645), actually in the Dulwich Picture Gallery, UK.