There seems to be an anomalous "jink" in the parish boundary just west of the station taking the railway into Woodley all the way east to the Loddon. Looks like you pass into Earley as soon as you step out of the station.
Amazing how Berkshire local government boundaries feature in this forum - see Green Park Station forum for more......
In 1933 Earley parish was a lot smaller. Woodley and Sandford parish ran to the Loddon (across which lay Winnersh parish, as now) and down into what's now Lower Earley but was then open country (apart from the ribbon development along Wokingham Road). The boundary with Earley was as now to the west of the station, then after turning south it kept going. Evidently when the boundary was moved to extend Earley to and a bit past the main road, they felt there was no need to go further than the southern edge of the railway land.
So the reason for the odd wiggles is the same as at Green Park station.