>>> Rail staff are obliged to offer the cheapest options as long as you ask for them.
'Fare-splitting' is common practce and there are even websites which try to do it for you, such as this one:
http://www.splitmyfare.co.uk/
However they're not perfect. I've often been able to beat their quotes by doing it manually here:
http://www.nationalrail.co.uk/
(and those 'split fare' websites usually seem incapable of breaking a journey into more than two separate sections).
The only thing to watch out for when opting for 'fare-splitting' is that the train you take (if it's a through one) must stop at the station where one ticket's validity ends and another one's starts. e.g. if you found that it was cheaper to get from Swansea to Paddington by paying from Swansea to Newport and then from Newport to Paddington, you'd need to ensure that the Paddington service that you boarded at Swansea actually stopped at Newport.