The references to "Elizabeth Bennet" and "Pemberley" is to Jane Austen's 1813 novel, "Pride and Prejudiice."
Robert mentions the family owns paintings by Romney, Reynolds and Winterhalter; he is referring to George Romney (1734-1802), Joshua Reynolds (1723-1792) and Franz Xaver Winterhalter (1805-1873). All three artists were known for their neoclassical portraits of upper-class society and their works were popular with British peerage of the early 20th century.
The open house tour and conversation afterward among the family seem to be a winking foreshadow of the future of the actual house, Highclere Castle, as a filming location. As of 2018, it's open to the public each summer and other times during the year.
Mrs. Crawley, played by Penelope Wilton, mentions that "Even Elizabeth Bennett wanted to see what Pemberley was like inside." Wilton also played Elizabeth Bennett's aunt, Mrs. Gardiner, in Pride & Prejudice (2005). During their leisure travels, the Gardiners persuaded Elizabeth that the three of them should tour Pemberley while Mr. Darcy was away.
The house is open to the public for '6d' (6 pence) as shown on the flyer posted in town. This was before Decimal Day (February 15, 1971) when Britain decimalised its currency and the pound was divided into 100 "new pence," each of which was worth 2.4 old pence. Converted into new pence that's £0.03. Adjusted for inflation, £1 in 1925 is worth £42.45 in 2021. So the price of admission is now £1.27. The price of admission to Highclere Castle in 2022 is £27.50.