Trains, buses and taxis
Trains
London Paddington - Reading - Didcot Parkway 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, 15 to Didcot Parkway (change for Oxford) and 50 mins to Paddington (or change at Reading and 30 mins from Reading)
Here is the GWR timestables. Didcot Parkway-Paddington, the servive through Pangbourne is Timetable TW10
Going Forward Buses - The Parks Route (145-148)
Goring to Reading through Pangbourne and Whitchurch. Details here.
Other Going Forward bus details here.
Bus Service 143 - Thames Travel
Bus service between Pangbourne and Reading along Oxford Road: the timetable is here.