Thanks for the link.
Thomas Catling enlarged upon the timing details, writing–
"A subsequent comparison of times [between Lloyds Weekly News and Catling hearing of the murder] showed that the man who conveyed the first news to the office must have been on the spot within five minutes of the discovery, and then walked very rapidly to Salisbury Square."
As the crow flies, Salisbury Square is about 1.25 miles from Mitre Square, so Lloyds Weekly News hearing of the murder at 2.10 am sounds perfectly reasonable to me.
Someone was on the ball on this night of nights.