Is it not Eltham Street? Which is in Newington, the Walworth area. But there are various references to this street in the newspapers as Eltham Street, Borough or Southwark or Old Kent Road, even Eltham Street, Bermondsey.
The main occupier in 1901 is William H Baker, 74, born Truro Cornwall. Widowed with two daughters. Also George + Sarah Farmer. Piece 381 Folio 37 Page 12
Mr Baker had been at number 23 for many years (is there in 1881). But he's not on the electoral rolls there after 1902?
One idea - probably wrong, but there's seemingly no "normal" answer - there is a Jessie Toon in Lambeth in 1901, age looks like 30 to me, it could have been altered, born Devon. Married to Thomas, 38, a Plate Layer from Northampton
Except that they aren't married. He had been, and his wife Sophia Julia had died in 1899. Thomas seems actually to have been born in Islington circa 1859, and he had a married sister Ellen Ruskin with whom his daughter Elizabeth was supposed to have been staying in 1900 after she came out of the workhouse school (this from poor law records).
Thomas and Jessie have a young son in 1901. And Elizabeth is back home with her father again. After which they have all disappeared. Can find no one at all, which does not help the following theory. But I just wondered if Jessie Toon was a married name (even if not legally so) which was later dropped. In other words could this Jessie have split up with Thomas Toon and then lived with someone else? If this coincided with the murder case and its publicity, it would put her in an uncomfortable position if she didn't want her affairs to be known by everyone. So she remained as Jessie Toon while the case was going on and Frank Mcguire or whoever he was had to be referred to by her as Frank Toon?
But whatever, thats what I am suggesting anyway, maybe your lady had at some time been known as Jessie Toon but Frank wasn't a Toon at all. And no Frank and Jessie to find in 1901