The National Routing Guide sates, in the instructions section:
"Most customers wish to make journeys by through trains or by the
shortest route. In both cases they will be travelling on a permitted route,
provided the correct fare has been paid to reflect any routeing indicated by
the fares manual."
In this case, the tickets are all routed any permitted, so assuming the trains are through trains there is no problem.
A through train is defined in the gloassary of the National Routing Guide as:
"Through Train
A through train is one which runs between the origin and
destination stations and on which passengers can make their
journey without having to change trains."
This service does run through from Romsey to Southampton, and hence passengers can make that journey without changing trains. Note the use of the word can, implying only that this needs to be possible, not complusory. As long as the journey is resumed at Eastleigh, this condition is fulfilled on both counts.
A though train is not defined in the NRCOC, either in clause 13 or Apendix A, but I think the only reasonable interpretation is the same definition as the routing guide.
The NRCOC has this to say on breaking of journeys:
"16. Starting, breaking or ending a journey at intermediate stations
You may start, or break and resume, a journey (in either direction in the case of a
return ticket) at any intermediate station, as long as the ticket you hold is valid for
the trains you want to use. You may also end your journey (in either direction in
the case of a return ticket) before the destination shown on the ticket. However,
these rights may not apply to some types of tickets for which a break of journey is
prohibited, in which case the relevant Train Companies will make this clear in their
notices and other publications."
Now, SWT have made clear in a notice at Romsey station, and presumably others at which the same situation occurs (can anyone confirm this). However, the other clause is "and other publications". The only time that the SWT website mentions break of journey is in relation to advance fares, which are not relevent here. The Great Western website does not mention break of journey. The National Rail website, in the Anytime Day terms of conditions states:
"You may start, break and resume, or end your journey at any intermediate station along the route of travel." Which to me is fairly conclusive.
In the off-peak day tickets terms and conditions, it states:
"
Break of journey is allowed on Off-Peak tickets unless restricted for the journey you are making. If you intend to break your journey, please call 08457 48 49 50 to check if it is available on your specific journey.
If you break your journey and are still travelling at 0230 then you may stay on the train to complete that part of the journey, but no further break of journey is allowed and all travel must be completed by 1200."
The restriction code of the off peak day in Avantix for this route does not show any restriction on break of journey. Perhaps somebody could confirm whether that is also the case in the FRPP. Assuming that is the case, the advice given on telephoning the number given on the National Rail website would be that a break of journey is allowed. This would also be the case if you asked a booking clerk at another station, or if a guard looked up the ticket on his machine.
Of course, FGW could quite easily ban break of journey on the cheap day return by changing the restriction. However, in my opinion this would have to be published clearly in the journey planners and in the ticket desciptions on the Great Western and South West Trains websites. To alter the validity of the standard/first day tickets would require a change in the ticket terms and conditions nationwide.