The Duchess is filthy! The first coach appears to be a ex HR vertically boarded corridor coach, it does not quite look right for a LYR one and has passengers on board so is a strengthener. Note the LNWR signal wire 'compensator' with balancing weights for 3 signals, it must have been a long pull to the outer distants!
A fascinating and rare image. This is confirmed by Ian R Townend as 6232 in early post war period after fitting of smoke deflectors but still in LMS red. This dates the photo to the summer of either 45,46 or 47

The train appears to have reporting number W97 which would be the down Mid-Day Scot so what on earth is that first carriage doing behind the tender!