First of all, unpublished works from the 1920s, even before 1923, would not yet be in the public domain. (You probably wouldn't be calling it a "newspaper illustration" if it wasn't published in a newspaper, but this rule still matters for one special case I'll get to later.)
If the work was originally published in the US, or was published in the US within 30 days of its original publication, then something published in the 1920s could be public domain in the US if one of the following is true:
- The work was published before 1923. (In the US, the date of death of the author does not matter for works published before 1978.)
- The work was published without a copyright notice.
- The copyright was not renewed.
If the work was originally published outside the US, other rules may apply:
If the work was published before 1923, it would be in the public domain under US law. However, if it was published in a language other than English, then in some states it was treated as unpublished until it was published in compliance with US laws.
If the work was created by a resident of a country such as Iran that is not a party to copyright agreements, the work is unprotected by US copyright law.
For most other countries and circumstances, it depends on whether it was in the public domain in its home country in 1996 (or some later date, if the country didn't join the Berne Convention or the WTO until later.)
Given UK copyright law, if this work was originally published in the UK in 1923 or later, it would probably still be copyrighted in the US, since it would have been copyrighted in the UK in 1996.
There's something else worth noting. In the US we haven't had any old works enter the public domain in the last 20 years due to a retroactive copyright extension. However, in 2019, assuming there's not another retroactive extension, works from 1923 will enter the public domain. By 2025, all published works from 1929 and before should be in the public domain in the US.