While I can't say this is the same for GWR or not, for my local train service regardless of what station you got on at / are getting off at, whether you are allowed bikes on it or not applies to the times it reaches wherever the end of the line for that train is (whether that is London, Reading, or somewhere else).
Which can mean you get the slightly odd circumstances of the rules saying no full size bikes allowed between 1630 and 1900, but although your journey finishes at an intermediary station outside of these times (e.g. 1615), you can't take your bike on it, because the train carries on and reaches its final destination at 1645, which falls within the restricted times.