Posting on Twitter at 7.52am, the council announced a further recount is required, and will be carried out "as soon as possible."
Reports suggest the result may not come in until this afternoon or maybe even tomorrow (Saturday June 10).
The Kensington constituency is the final result to come in from west London.
In a statement, returning officer Tony Redpath said: "The provisional result of the election was known at approximately 2am. That result was very close and a recount was therefore requested.
"The result on that recount also remained very close.
"A request for a third count was therefore made. At this stage staff had been up all night and were becoming visibly tired. In order to have confidence in its accuracy, the recount has been suspended to allow staff to rest and recuperate.
"The count will recommence as soon as possible and details will be posted on our website and on social media."
On Twitter, the Royal Borough of Kensington and Chelsea said would the count would resume either later on Friday or Saturday.
Across the west London boroughs , there have been some Tory successes, with Greg Hands celebrating a reelection in Chelsea and Fulham , and Mark Field holding his seat in the Cities of London & Westminster constituency.
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