If you've booked what's descibed as "Advance Single" tickets, then:
VALIDITY
You must travel on the date, time and trains specified. You may not start, break and resume, or end your journey at any intermediate station except to change to/from connecting trains as shown on the ticket(s) or other valid travel itinerary.
But if you've booked "Off Peak Single" tickets in advance then:
VALIDITY
Your journey must be on off-peak trains on the date specified. Off-peak times vary by route - our journey planner only shows off-peak tickets on trains for which they are valid.
In other words ... with the second type of ticket, even though it says "Routes via Slough" you are allowed to get off at Reading and cut your journey on that ticket short there. You could then buy a separate new ticket onward from Reading. I'm not sure if you would be allowed to resume the previous ticket's use at Redhill, or have to use fresh tickets all the way from Reading to Eastbourne.
With the first type of ticket, you must use it on the specified train all the way to Paddington. Technically, even if one of you was taken ill in Reading and you had to be taken from the station to hospital by ambulance, you would have to buy fresh full rate singles from Bristol. You could even be penalty fared as you tried to leave the station / change trains going off your original ticket.
In general, "Advance Single" tickets are very limited indeed in changes that can be made to your journey, and you should only book them if you are certain of your journey times, joining and leaving points, or if you are prepared to take the risk of loosing all or most of your money if you get it wrong, or if circumstances outside the control of an
ATOC» member conspire to have you miss your train.