I'm quite surprised that this is the case, but there are indeed Off-Peak fares from London in this time frame!
Assuming you're going out on an Off Peak Day Single or Off Peak Return (Day or otherwise, either portion), you can apparently catch the following trains from Paddington for travel to Reading.
17:06 to Westbury
17:18 to Oxford
17:24 to Banbury
17:36 to Oxford
17:57 to Reading (*Overtaken by a later train that allows Off-Peak ticket holder to travel)
18:05 to Frome
18:18 to Oxford
This is confirmed by VTEC website and the BR Fares website (Restriction Code 5K is in force).
As above, it would be worth confirming which ticket you hold to clarify which of these services are definitely valid for you.