Trains, buses and taxis
London Paddington - Reading - Oxford local services, operated by Great Western Railways, call at Pangbourne Station, which is 5 - 10 minutes walk from Whitchurch-on-Thames.
Trains run about half-hourly - journey times are about 10 minutes to Reading, 30 minutes to Oxford and 1 hour to Paddington (or change at Reading and 30 mins from Reading)
See the live departure board at Pangbourne Station
Bus Service 142 - Going Forward Buses - Saturday only
FROM AUGUST 2018 THERE IS ONLY A SATURDAY SERVICE
See here for more details. This is called the Parks Route - this service runs from Goring to Pangbourne, to Whitchurch, Crays Pond, Woodcote, Caversham, Tesco and the centre of town and back again.
Other Going Forward bus details here.
Bus Service 143 - Thames Travel
Bus service between Pangbourne and Reading along Oxford Road: the timetable is here.
Here is a useful link which gives a list of registered taxis, insert your postcode and it will give local taxi firms.