No you're not.
Not quite as simple as that. It depends whether you take the restrictions on Advance Purchase tickets as being more important than the National Rail Conditions of Carriage.
NRCoC▸ allow you to buy multiple tickets for
one journey, so should you be delayed on the first part of your journey (provided you catch your first booked train) then I would expect the railways to honour the NRCoC and allow you later travel on the second or subsequent parts of your journey. NRCoC makes no destinction regarding the type of tickets held. As long as you have allowed sufficient time at your interchange station (24 mins at Reading is more than enough) then I'd say you are fine to catch the next train if you missed your booked one through a delay to your previous leg.
Over at RailUK Forums this subject crops up with regularity and the two schools of thought are both passionately argued. There's plenty of evidence there from on train staff that they are happy to allow later travel as long as it was the railway that caused the delay. I, too, am in the camp that NRCoC takes precedent.
Should you experience a problem by not being on your 2nd booked train, with on train staff who say you are not valid to travel, then I'd suggest only accepting a
UPFN▸ and not parting with any more money.
Unfortunately it's not in the
TOCs▸ interests to provide a definitive answer when it comes to using split Advances, so we are only really left with what the NRCoC says:
19. Using a combination of tickets
You may use two or more tickets for one journey as long as together they cover the entire
journey....
I'm attending a Fares Symposium with members of RailUK Forums in a couple of weeks time and I've no doubt that this issue will be high up the agenda!
If you'd like to read more on both interpretations then try this:
http://www.google.co.uk/#sclient=psy&hl=en&q=combination+of+tickets+advance+site:railforums.co.uk&aq=f&aqi=&aql=&oq=&gs_rfai=&pbx=1&fp=1&cad=b