The train slows down between Hyde Park Corner and Green Park as it passes through the now closed Down Street station.

The platforms of Down Street have been bricked up but otherwise the station is still there. You can tell you're passing through it when the train slows, and the wall changes to brick for several seconds. You can also see some kind of junction before the platforms. If you walk along Down St on the surface you can even see the old station facade still there.

https://www.google.co.uk/maps/@51.5046265,-0.1477147,3a,75y,...

This guy has a very detailed map of the underground system including closed/defunct stations: http://carto.metro.free.fr/cartes/metro-tram-london/