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A spokesman for Britain's anti-terror police said in a statement that British investigators relied on trust with security partners around the world.
"When that trust is breached it undermines these relationships and undermines our investigations and the confidence of victims, witnesses and their families," he said.
"This damage is even greater when it involves unauthorised disclosure of potential evidence in the middle of a major counter terrorism investigation".
Contacted by AFP, Greater Manchester Police declined to comment on the BBC report.
The New York Times published on Wednesday what appeared to be police photographs showing fragments from the bomb and a backpack used to conceal it.