The figure is a big increase compared to the previous police estimates that 500 people were hurt in the Manchester Arena attack on May 22, in addition to the 22 killed, British media reported.
"We knew quickly 22 people had been murdered and we now know that there are over 800 people with physical and deep psychological injuries from the attack.
"Their lives have been altered forever," he said.
Jackson gave an insight into the size and scale of the investigation almost a year on from the suicide bombing, claimed by the Islamic State terror group.
The investigation into the bombing has so far cost 4 million pounds from the counter-terrorism budget.
Police is awaiting the extradition of 21-year-old Hashem Abedi, the younger brother of Salman from Libya. No one has yet been charged with helping Abedi.
Twenty-three people were arrested in the days and weeks after the attack and all were released without charge. No one has since been interviewed under caution in relation to the case. Jackson said 2,000 witness statements had been taken.
Jackson said the investigation team had worked hard to support those affected and had been "consistently moved by the grace and dignity they show in trying to repair their lives".
"Of course for many, the loss is too great for them to ever make a full recovery from this terrible event."
A team of about 100 investigators are still working full-time on the murder investigation "preparing for a trial".
Jackson said it was "really difficult" to give an update on the progress of the extradition of Abedi's brother Hashem, who is currently in custody in Libya.
A warrant for Hashem's arrest over allegations of murder, attempted murder and conspiracy to cause an explosion was also issued before the extradition bid on November 1, 2017.
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