Think the train shown was the (Saphos Trains Ltd) "Settle and Carlisle Fellsman" which in 2023 is scheduled to operate four times during the year and normally starts out from Crewe at 0700 with pick-ups at Chester, Frodsham, Warrington Bank Quay, Wigan North Western, Euxton Balshaw Lane, Blackburn and Clitheroe, before accessing the Settle & Carlisle line at or shortly after 1030 and arriving in due course in Carlisle at around 1315.
Return from Carlisle is at 1545, arriving back in Crewe at 2200.
Pullman Dining (if not already sold out for 2023) was available at £350 per person (plus £40 per person for two "guaranteed" window seats) so whilst expensive, it's still cheaper than an Anytime First Class return in the other direction, from Crewe to, say, Watford Junction.