Oh, no, not that can of worms again!
An hour is pretty standard but if you get off the HST near the rear of the train (can't remember which coach), go straight up the stairs to the H&C platforms and get on a train pretty quick, then I'd say you stand a chance of getting the 1459, although whether you are allowed to or not is debatable. You should make the 1505 which there is no doubt you are allowed to get. The 1515 is debatable.
If the ticket was routed "FGW & Connections" then the vast majority of people (including many railway staff) would say you can take any train. Of course HHF would disagree but that's only to be expected
However as it doesn't, then there is no rule stating that you can take "appropriate connecting trains", only that you can take "booked trains". This of course led to the debate a few weeks/months ago as to whether or not a train that is merely "suggested" is "booked" or not. It's a massive can of worms and the rules are not totally clear one way or the other. Given the lack of clear rules, it will be up to the guard to make a decision based on what he/she thinks the rules are. I cannot predict how they will react.
My advice would be to approach the guard and ask "Am I OK to use this ticket on this train?" if they say no, head to the FCC train 6 or 10 minutes later.
It's only an extra 17 minutes on FCC (+ 6 or 10 mins wait).
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Contrary to the previous poster, the answer is almost certainly yes as long as it is FCC.
I agree that the previous poster is incorrect, although it is debatable whether it has to be FCC. The ticket itself isn't a FCC/FGW specific ticket.
East Coast services allow booking in their own right so you may well get a problem if you use them.
Although there isn't a rule that states that, and I disagree with people who claim there is such a rule, I agree that there may be issues in practice.
With FCC the guard is unlikely to be interested in working out whether you have made quicker time that allowed from Paddington.
There isn't a guard, and as there is no reservation an RPI could not know what train you were 'advised' to get and I agree they wouldn't be interested in working it out.
The tickets will not give details of the FCC train, only the FGW train is listed on the reservation coupon.
Yes, normally on this type of ticket I'd expect the system to 'book' an EC service, but the engineering works on that Sunday mean that there is a huge gap between 1515 and 1659 with the only train between them the FCC train the OP is recommended to get.