I showed LNER and BR(E) Pullmans with Clive in separate chapters and there are updates on the w/s for the "Queen of Scots" and the "West Riding/Yorkshire Pullman" which ran through Yorkshire (see links below). This is for one of the others.
The Sheffield Pullman LNER
The Sheffield Pullman was short lived and ran in 1924-25, initially from KX to Sheffield, then from Sheffield, and finally, from Manchester, see pages 113- 115. Pullman trains were so heavily photographed that a casual look can give the impression that they were the most numerous trains on the line. The "Sheffield Pullman", however, was so short-lived and travelled to the GC Section that few pictures were taken and they are quite rare, and often miscaptioned. Because it ran so early in LNER days, it was made up with "white" Pullmans.

This picture was used in the book but got cropped quite heavily to emphasise the carriages and the exhaust darkened - it is quite a tricky and dark image. Here is a wider view. The 5-car formation included a Kitchen 1st, two Kitchen 3rds, and two 3rd brakes whose design (between 8- and 12-wheelers) was changed. This is the original formation with four 12w cars and one 8w. Photographed during the first week of operation in 1924 at Woolmer Green behind ex-GCR Robinson B2 No 425 City of London. Photo: Author's collection.
Click on the image for an enlargement

This picture was taken a little later in the summer of 1924 with C1 No 3301 (KX) in charge and is unusual because one of the 12w cars has been replaced by an 8w design, making two in the train. It wasn't long before older 12w cars made up the whole train. Photographed at Hadley Wood (and miscaptioned as "c1930" and in modern biro, the "West Riding Pullman"). Photo: Real Photographs.
Click on the image for an enlargement
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