I used to live in Woodley - part of Wokingham District Council but actually in Reading and the traffic was always dire - the bus, taking the train, cycling or walking seemed faster.
And drivers never seemed generous - saw many, many prangs in the city centre as a result of this.
And Bracknell is not a nice place - all 1960s nameless facelessness. Mr MLG used to work in Bracknell. Ugh.
Maybe give a few different routes / methods a try during rush hour to compare?
I know nothing of Wallingford. Sorry.