The London and North Western Railway Society tells us the history of Uppingham station:
The London & North Western Railway opened this short branch in 1894. Five trains were provided daily all connecting with services to and from Rugby. Passenger services were withdrawn in 1960 but the station remained open for school specials until the line closed to all traffic in 1964.It also says
The site of Uppingham station is now a small industrial estate but the goods shed and stables survive.I went to look for them after travelling to Uppingham on the 747 bus. I didn't find the goods shed - it may not still exist - but the photograph above shows the former stables.