The copyright would have been with the company rather than the artist? Which became the TOCs ?
Lots of prints are available online. The Science Museum collection has a free for non commercial use licence.
Who owned/owns the copyright and how long the copyright lasts (“duration”) are two different things.
As a rough rule of thumb take
duration of copyright as stated by
@hexagon789 - life of creator plus 70
full years (i.e. to the 31st Dec of the 70th year after the creator died.) This does vary, especially in the case of graphical works (such as posters and their artwork) but if you assume death+70 that’s a good start. So, for any poster images older than 70 years after the death of the artist you can generally (not always) assume they are out of copyright.
Ownership of the copyright depends on the contractual terms (if any) under which the work was created and any subsequent deals - copyright is a property right, separate from ownership of the actual physical copyrightable object, and can be bought/sold/gifted on its own.
If the poster artist was commissioned by a (railway) company they may have contracted with the artist that the company would own the copyright of any artwork they bought, as well as the actual physical artwork. Alternatively the artist may have insisted on retaining copyright and just licensed the artwork image to the railway company for a specified period/set of uses. Without knowing the terms of the original contract you can’t say. And then the artist or the railway company may have sold or gifted the copyright to someone else.
In the case of posters held in the Science Museum/NRM collection, the British Railways Board gifted any copyrights in those posters (or inherited from the pre-nationalisation companies) to the Trustees of the Science Museum
insofar as BRB owned them. Whether the BRB actually
did own the copyright for every individual poster is debateable. But unless anyone else claiming to be the copyright owner makes a fuss we won’t know. And as the posters age, so the issue diminishes.
As a public good the Science Museum has decided to let people have (low-res) copies of the images free for non-commercial uses. But if you want to use them for commercial purposes (e.g. selling reproductions for framing, or for model railway use) then you’d need to determine the copyright status.