I've said it before but I seem to have been asked to say it again - most information about old tool history is NOT available on-line. You need to look at books, magazines, catalogues, and the tools themselves.
The standard reference work for identifying and giving approximate dates to planes is "British Planemakers from 1700" by WL Goodman. The best version is the third edition, revised by Jane and Mark Rees, published in 1993, commonly called BPM III. Frustratingly for many new collectors, the book has been out of print for some time and prices of second hand copies are still going up. Jane Rees is working on a fourth edition, but it's a huge undertaking and she can't make any promises on when it will appear.
BPM III attempts to put makers' marks in chronological order. It shows your mark - on the swirly banner - as being the last one used but does not put start and finish dates on its use - that's just not possible.
The 1938 catalogue, as you say, refers to the Shamrock mark, on every page. Interestingly, it also shows that marks were a tradable intellectual property - by that time Marples had begun absorbing other companies, so if you wanted your plane to be marked with the name of the earlier London maker John Moseley, you could, for the same price.
This page shows that they also owned the Ibbotson mark - there was a lot of this sort of thing going on in Sheffield.
Marples were the last big firm to make wooden planes. They carried on until 1965 when Ken Hawley acquired their production tools, which are now in the Ken Hawley Gallery at the Kelham Island Museum in Sheffield. So, at a very rough guess, your plane is probably somewhere after 1938 but before 1965.