Its title is a reference to the Horse of the Year Show, because equestrianism is often regarded as an upper-class pursuit in the UK.
The obstacles are, in order: The sketch ends with Gervaise Brook-Hampster coming in first, followed by Smith-Smythe-Smith (shot by Nigel in ANFSCD, shot by Simon in MPFC) and Nigel Incubator-Jones in a medal ceremony, while Simon Zinc-Trumpet-Harris manages to club himself unconscious with the butt of his gun (in MPFC, the men also are interchanged).
Cleese ends his commentary by remarking that "there'll certainly be some car door slamming in the streets of Kensington tonight!"
John Cleese has stated that the idea for the "wake the neighbour" part was inspired by an apartment he once rented that was near a bar whose patrons kept him awake at night when they slammed the doors on their cars.
[2] This is also mentioned in trivia notes included on the A&E DVD release of Season 1, though the wording there suggests the entire sketch may have been inspired by the people Cleese encountered, not just "wake the neighbour".