Putting aside for the moment that David Pardo, the Hazzan in London, only published it, but actually his father Joseph was its author - the note states that in the Seder Ha-doros of Rabbi Yechiel Heilprin, 18th century Minsker ga'on and historian/bibliograpaher par excellence, the author of Shulchan Tahor is given as Baer London. And indeed it is.
The excerpt I reproduce above is from the original, first edition of the Seder Ha-doros (Karlsruhe 1769). As it happens, Felsenthal says he used the Warsaw 1882 edition. In any case, Felsenthal explains what happened - or as we shall see, what he thinks happened. Rabbi Heilprin looked at the title page and must have read it quickly for he read "בער לונדן" (Baer London) instead of "בעיר לונדן" (in the City of London), to say nothing of not having properly read that title page at all. Here is the title page of the 1686 Amsterdam edition:
So it says "Printed at the behest of the scholar, sweet singer of Israel [i.e., Hazzan] in the City of London, Rabbi David Pardo." But Heilprin misread - perhaps jotted down a note without looking carefully - and read "be-'ir london" ad "ber london." Adding some flourishes, Felsenthal makes a big deal out of this interesting error and exaggerates that this man who never existed, Baer London, was "made immortal" by Heilprin. Okay, very cute.
In any case, as I said, Felsenthal had the Warsaw 1882 edition in front of him, and he says that here the Seder Ha-doros mentions Baer London twice; once in his list of books - which I showed above - and once in his list of authors. Interestingly, if you look at the 1769 edition you will see that Baer London is not listed among the authors. Here is where Baer London would be listed in the first edition, but he isn't:
These are all the Baers that Heilprin listed as authors.
If you examine later editions, you will see the same thing. So here is the 1858 edition:
And also, there is no Baer London. Baer London is only mentioned in the entry for Shulchan Tahor proper.
However, in the Warsaw 1882 edition we find the following:
Here we see him listed as an author. However, he is in parentheses and the reason is because he, as well as others, were added by the learned editor of this edition, Naftali Maskil Le-Eisan. In other words, the editor of this edition improved upon the earlier ones and added author names missing from the text and the list compiled by Heilprin. After all, if Baer London appears in the list of books, should not his name be given as one of the authors? So although Heilprin did, seemingly, make an error and read "City of London" as "Baer London," he didn't quite immortalize him. More like squeezed him into a lengthy paragraph.
But in any case, it turns out that Heilprin probably made no error at all. No, there was no Baer London. But surely he was capable of reading a simple inscription on a title page, if not the work itself. It turns out that in 1696 a second edition of Shulchan Tahor was published in Franfkfurt. Unfortunately I do not have access to the title page of this edition, however in a wonderful article from 1928 Israel Solomons seems to have independently noticed the same thing as Felsenthal, but he knew more about the Shulchan Tahor itself. In David Nieto and some of his Contemporaries Transactions (Jewish Historical Society of England) , Vol. 12, (1928-1931), pp. 1-101, Solomons writes as follows:
As you can see, whomever put together the 1696 edition somehow managed to misread the title page of the original 1686 edition, and it was that person who read be'ir london as ber london. That person seems to have omitted David Pardo's name, and replace it with "the wise scholar Rabbi Baer of the Congregation of London" (מהרר בער מק"ק לונדין) - which was accurate insofar as Pardo was in London, it just made him Baer. I can only assume that Rabbi Heilprin had before him the 1696 Frankfurt edition and wrote just what it said on the title page. Sure, he omitted מק"ק, but so what? The 1696 Frankfurt Shulchan Tahor said it was printed by Rabbi Baer London, and that is what is repeated in the Seder Ha-doros. The editor of the Warsaw 1882 edition improved it and added all the various author names in the text proper to the list of authors cited in the Seder Ha-doros. If Baer London was "immortalized" it was by Maskil Le-eisan, who plucked a name buried into a paragraph and gave him a real entry. Note that Solomons tells us that the 1696 edition did not even include the introductory paragraphs, that is, all the stuff by and about Pardo. So it is likely that Heilprin did actually read the Shulchan Tahor, it is just that his edition had nothing about the author apart for the mistake on the title page.
Finally, it should be noted that Solomons says that actually it doesn't even say Frankfurt on the title page, but that is what bibliographers say about it. So, for example, we find in the 1826 catalog of the Oppenheimer Collection (Collectio Davidis):