And experts fear the virus could spread to internationally significant populations of other types of birds coming to the UK.
Last month, wardens in white suits collected around 3,000 bird corpses from the islands.
Now that number has risen to 5,000 - but the rangers say actual deaths could be 10 times that number, because many carcasses will not yet have been found.
The islands, a national nature reserve, are an internationally important habitat for 23 species and home to about 200,000 seabirds, including guillemots, kittiwakes, razorbills and shags, as well as Arctic terns and puffins.
Gwen Potter from the trust, which cares for the islands, said they had not seen anything like it before and that cliff-nesting birds such as guillemots and kittiwakes were among the worst affected.
Half the islands’ sandwich terns have died, she told Radio 4’s PM.
And she called for more government resources to investigate bird flu transmission and an action plan for all four UK countries.
Fears are rising that bird flu will continue to spread and devastate seabird populations. More than 300 outbreaks have been reported in British colonies so far.
Tom Stewart, of the British Trust for Ornithology (BTO), told The Times: “There is no doubt that this outbreak of avian influenza is the most severe ever recorded among British wild birds.
“We have now come to the time of year at which these colonies begin to break up, with birds dispersing around this country and elsewhere.
“There is a serious risk that these movements, which we are not able to control, will introduce avian influenza into other bird communities, including the internationally significant populations of wintering waders and wildfowl that have already begun to arrive in the UK.”
Some scientists say intensive chicken farms are potential “mixing pots” for new, deadly viruses, and animal charities have blamed factory farming for fomenting bird flu.
The RSPB has called for an immediate suspension of the release of gamebirds and wildfowl for shooting in the UK, warning they could spread the disease to even more species.
Pheasants in the UK have tested positive for bird flu 14 times, the charity says.
The death toll will not be known for some time as seabirds are long-lived and slow to reproduce. “Only long-term monitoring will reveal whether they are able to recover,” Mr Stewart said.