Up until June 1957, the applicable law at the time these poetry books were published was the 1911 Copyright Act. While section 5(a)
of that Act did make certain provisions about commissioned works which resulted in the ownership of the copyright passing to the person who commissioned the work, this only applied to certain artistic works such as engravings, photographs and painted portraits. Literary works were not covered by this provision.
So unless the authors of the introductions signed over their copyright to the publishers, it would have remained with the authors. While it is not unusual for publishers to insist on a contract which transferred copyright to them, either for a finite period of time or for the duration of the copyright, it cannot be assumed that that was always the case.
Either way, the duration of the copyright protection is determined by the lifetime of the author plus, initially, 50 years. Given that these authors must have been alive in the 1940s and 1950s, it safe to assume copyright in their contributions ran at least until the end of the last century. This means that the introductions were still in copyrght at the time (1 January 1996) when an extension to the term came into force, adding a further 20 years to the period. Therefore unless an author is known to have died before 1946 these introductions are still likely to be covered by copyright.
The problem you face is tracking down the putative owners of the copyright, either the publishers, or the authors or their heirs. As, quite often publishers' contracts contained reversionary clauses which transferred any copyright back to the estates of authors on their death, I think the more fruitful line of inquiry is to try and find the authors or their heirs. If after conducting a dilligent search you cannot locate any heirs, you should be able to apply for an orphan works licence
to use these introductions without incurring any liability for infringement should an heir subsequently come forward. Realistically, unless these authors left extensive literary estates, it may well be that no-one alive today realises the significance of any copyright protection. The government's Intellectual Property Office has published a helpful guide
(pdf) on how to conduct a dilligent search concerning literary works.