For example, would people in England in 1800 have known what the Mona Lisa looked like?
sure. but also remember your forgetting copying. David mcculloch (american popular historian) wrote a recent book about american expats in paris in the 19th century and it includes Samuel Morse (of morse code fame) who made a famous painting of the louvre galleries composing its greatest hits and this was a big success in the states. Given the proximity i'm sure reproductions would have been available in england in a similar way especially since aspiring painters would go to art museums and work from the great paintings.