Claydon was opened by the Buckinghamshire Railway on 1 May 1850 as part of its line from Banbury to Bletchley. The line was worked from the outset by the London and North Western Railway (LNWR) which absorbed the Buckinghamshire Railway in 1879. The line was subsequently extended westwards to Islip, to a temporary station at Banbury Road and then to Oxford, opening throughout on 20 May 1851.
Claydon station was situated at the 11 milepost on the eastern side of a level crossing where the road from Steeple Claydon to Middle Claydon crosses the line. The station's name came from the fact that the location is surrounded by places with "Claydon" in their name, such as Botolph Claydon and East Claydon, as well as Claydon House which was the residence of Sir Harry Verney, one of the founders of the Buckinghamshire Railway. The nearest village was Steeple Claydon whose inhabitants also had the choice of Padbury railway station on the Banbury to Verney Junction Branch Line which was about 2 miles (3.2 km) away.
The cost of the station was £1,000 in respect of building work plus £200 for machinery. Two platforms were provided with the station buildings on the "Up" side and a timber platform and waiting shelter on the "Down" side. The stone "Up" platform was very low and also very narrow. The architecture was a rural combination of brick and timber with some restrained ornamentation. The station house which adjoined the platform buildings was in a similar style to structures on the Bletchley to Bedford section of the line, being built of brick and half timber rendered with cement and decorative barge boarding around the gables. A small goods yard was served by two sidings and comprised a loading dock, weighbridge, brick hut, ground frame and loading gauge. The level crossing gate and sidings were controlled by Annett's key; when the siding was in use it could only be released by a key which was kept in a gable wing of the station building. During London, Midland and Scottish Railway days, the station, which was in a relatively rural location, was served by six services in either direction on weekdays, plus an extra service on Saturdays and three services on Sundays. When the stationmaster at Claydon was abolished, two porter signalmen ran the station on alternate shifts.
In the wake of the abandonment of a plan to develop the Varsity Line as a freight link from the East Coast ports to South Wales, including a marshalling yard near Swanbourne, Claydon station was listed for closure in the Beeching report which called for the closure of all minor stations on the line. It closed to goods traffic on 6 January 1964 and to passengers on 1 January 1968.
The line will be reopened in the coming years but the station will not be reopened as part of the plans.