< To quote R.N. Coles on page 299 of the September 1954 BCM:

It is only more specific in that it names the Divan, but in Lowenthal's day, it was not perhaps not necessary to name the place, as it was well known that Williams frequented it habitually.

The center of the cholera outbreak was 1.6 miles from the Strand, according to Google Earth, and I traced his possible route that day to the Simpson's, and then to Charing Cross Hospital near the Strand.

There is some support for your theory if you read between the lines in the entry <When cholera broke out in London, he posted a notice on his door offering preventive medicine free. Supplies had run out, when feeling unwell, he left home for the last time, seized with violent pain in the Strand, he entered Charing Cross Hospital where he died of the disease two days later, leaving his wife and children destitute.>

He may have come into contact with cholera patients at his house, if he did not get water from the Broad Street pump himself.

About the location of some clubs.
From Hugh Alexander Kennedy 's "Waifs and Strays": the London Chess Club resided somewhere in Cornhill, the St.George's Chess Club in St.James' Street.

<The late Mr. Elijah Williams, the celebrated Chessplayer.— (From a Correspondent.) — This lamented gentleman was professionally a surgeon, but for many years had discontinued practice. When the cholera, to which he fell a victim, broke out, he benevolently posted a notice on the door of his house, inviting the poor to apply to him for preventive medicines, if attacked by premonitory symptoms, offering it to them gratuitously. On leaving his home for the last time, he asked his wife to give him some of the medicine, as he felt unwell. Unfortunately, the last bottle was exhausted. He walked to town, and was seized with violent pains near Northumberland House, in the Strand, and on the advice of a friend, went to the Charing-cross Hospital for relief. This occurred on the 6th of this month; on the 8th he expired in that establishment. Some of the medical men hoped that the crisis had passed; but Mr. Williams pointed to the blue marks on his nails. He was convinced, from this discoloration, that he would not survive. He has left a widow and four young children, utterly unprovided for; but his friends are raising a subscription for her support. It is hoped that this melancholy case, really worthy of Christian charity, will excite the sympathy of chess-players in particular. We urge the claims of the widow, the more earnestly, because we are personally acquainted with her truly deplorable position. Her youngest child is only eight months old. She is an amiable lady, deserving of aid in her sad bereavement.>

This correspondent, presumably Staunton, is evidently the source for Hooper & Whyld.

What's your source for this?

Here's one of its volumes (post-Williams):

Winter has this:

<An author and dramatist, Knowles edited the Illustrated London Magazine from 1853 to 1855. For a short time, Elijah Williams edited a chess column for the magazine, and on page 141 of volume one (1853) ...>

C.N. 9099

In 1853 Williams was certainly involved, at the start of the column at the very least:

https://books.google.com/books?id=J...

(Cf. the bottom right corner text)

Or even C.N. 9909

Knowles was the general magazine editor. It's not clear who he got to replace Williams, but I doubt he did it himself.

This should make things a lot clearer:

https://chessbookchats.blogspot.co....

OK, we now know Aug 1853.

<to his end,>

Pretty sure this is also wrong. Likely he only did 3 columns, as documented in the issue.