A quick update for everyone ---- it worked.
An Anytime Day return ticket on Virgin trains does indeed give you a Weekend First Upgrade (if travelling on a Weekend).
Funnily enough, the guards both ways wanted to charge us for a Weekend First upgrade, but after I'd asked them about the Anytime weekend upgrade and once they rechecked the tickets. they agreed that they were absolutely valid. Both guards said that they looked closely at the 'Class' of ticket, but not at they 'Type' of ticket.
I'm not 100% sure, but the type of ticket that is refereed
to here, may fit the qualifying criteria (it was advertised at Oxenholme today for £22.50 pp). Like the OP on the other thread, I can't find a reference for it online either !