If you don't mind a change, the "safest" way to ensure nice-ish trains between Oxford and London is to hop on the ~quarter past/to cross country trains and change for a HST at reading. Otherwise, look on something like realtimetrains or opentraintimes, and check the service details. If it shows as timed for "125mph max" / pathed as "Diesel Multiple Unit" or "High Speed Train (HST125)", normally OK. If it shows as timed for "90mph max" / pathed as "165/1 or 166 (Turbo) DMU", avoid!

Oh, and don't forget that tickets from Hanborough generally have more permissive off-peak restrictions and a greater range of off-peak tickets available than those from Oxford.