The modern rule in the UK is that copyright lasts until the end of the calendar year following 70 years after the death of the author. So if the author died in or later than 1953, it would be under copyright under this general rule.
However, this wasn't always the rule and the museum speaks of a copyright revived in the 1990s. So I went down that rabbit hole of historical UK copyright legislation. I personally find it interesting, but it turned out to not be entirely determinative.
It all turns on publication date and date of death of the artist, neither of which I can find, with the museum only stating the artist was active in the 1930s. But even assuming the most favourable facts for this to still be copyright under a "revived" copyright, the latest date I can find for copyright to still remain under that regime is end of 2015.
Per Copyright Act 1956 s. 3(4)(a):
in the case of an engraving, if before the death of the author the engraving had not been published, the copyright shall continue to subsist until the end of the period of fifty years from the end of the calendar year in which it is first published;
For the fact pattern I'm outlining, we must assume the author died before publication. As for the engraving bit, s. 48 defines that lithographs are engravings, and while I am far from an expert in this field, skimming the Wikipedia article on lithography, it does seem quite possible the poster could be a lithograph.
I'll note here since you bring up who precisely would be the owner of the original copyright, that it does seem likely that the poster was a work for hire, following the provisions of s. 4(2). As such, the copyright would have indeed ultimately transferred to British Rail.
Jumping ahead a bit, the more precise year which the museum states is "the 1990's" is 1995 (we'll get to why). So in order for copyright to have first expired as per the museum's statement and the authors active years, we must assume a publication date between 1930-1945 (or thereabouts, I'm not being super careful in this answer about the months things happen in, so there may be accumulation of off-by-one errors).
Because of those years, I now have to quickly address why the Copyright Act 1911 isn't relevant. The transitional provisions outlined in the Seventh Schedule reveal that only for photographs are the copyright duration provisions maintained from the 1911 Act.
Now we can jump into the modern law, the Copyright, Designs and Patents Act 1988 (CDPA). The transitional provision in the Schedule 1 s. 12(2)(b) directly maintains the 1956 copyright duration in this case which given our possible publication years, would have led to copyright expiry sometime between 1980-1995.
However, in 1995, the UK passed The Duration of Copyright and Rights in Performances Regulations 1995. This was in accordance with European legislation harmonizing copyright duration, in Directive 93/98/EEC (itself since replaced by Directive 2006/116/EC).
Side Note: 1995 is a peculiar year for copyrights in Europe due to that directive and so is exactly where I started my research for this answer, because it caused weird quirks for copyright terms in some countries in some cases.
For the UK, s. 5 of the regulation amended the CDPA, basically establishing the general European standard of copyrights expiring 70 years after the author's death.
More importantly for our case though is the regulations own section explaining in which cases the new copyright term expires. In s. 16:
The new provisions relating to duration of copyright apply— (a) [...] (b) [...] (c) [...] (d) to existing works in which copyright expired before 31st December 1995 but which were on 1st July 1995 protected in another EEA state under legislation relating to copyright or related rights.
Now, I'm not going to go through and look at all the EEA contries legislation to confirm, but it seems incredibly likely that one of them would have had engravings protected for life+70 in 1995, given that's what Europe has now standardized on (since we're assuming pre-publication death for an author who was active in the 1930s).
Notably, s. 17 even defines cases of expired works re-entering copyright as "revived copyright", matching the terminology the museum's statement used.
It would have been great if the 1995 regulation explicitly spelled out the relationship with CDPA's Schedule 1 s. 12, but in judicial interpretation, newer legislation takes priority, so the 1995 law would control.
Note: The answer is getting long enough so I'm not going to fully research/cite this, but for regulations vs. legislation, we have a weird case of a regulation amending a statute. I'm fairly certain this is due to UK Acts passed for European Community membership elevating regulations to primary legislation when they are passed for compliance with European law.
So given our assumed facts, the poster would have revived copyright per the 1995 Regulations. However, you may note (as I belatedly did after first posting this answer) that even given revived copyright, that revived copyright is still life+70. And the assumptions made for copyright revival under this clause requires a posthumous publication date of 1945 at the latest. This means at best any copyright under these particular circumstances would have expired in 2015.
There is a bit of a middle ground here. If the poster is not a lithograph, or the publication was not posthumous, the work would have gained a life+50 term per aformentioned Copyright Act 1956 s. 3(4). But then for copyright to expire and be revived, we still have to assume a 1945 death date at the latest.
Alternatively, instead of copyright revival, it could have gotten extended from life+50 to life+70 per the 1995 Regulations s. 16(c). But because we are more than 20 years from 1995, it mathematically works out that it doesn't matter anymore and we can just work with the life+70 rule.
A combination of 1995 Regulations s. 16(c) and posthumous publication though does actually give another reasonable way for the work to still be under copyright. If published in 1988 before the CDPA entered into force, it would have followed the cited 1956 rules of copyright expiring 50 years after publication. The 1995 Regulations s. 16(c) specifies that longer existing terms can continue. So that results in 2038 as a latest possible year through this method.
In the end I think there are two or three reasonable interpretations:
The museum is correct the work is under copyright, but incorrect about the reason.
- It's instead because the work is under copyright because the author died after 1953 (or is still living), or
- The work is still covered under the 50 years after posthumous publication rule for engravings established in the Copyright Act 1956 (publication years 1973-1988 for copyright expiry at the end of calendar years 2023-2038).
The museum is correct that copyright was revived, but I can't find a way for this to be true and for the work to still be under copyright (with 2015 the latest year I can find for the given facts).
Note that this is my own reading of legislation, please take it with a grain of salt.
