On Thursday four British meetings in Huntingdon, Doncaster, Ffos Las and Chelmsford, were cancelled.
The trainer concerned is believed to be Donald McCain, whose Bankhouse Stables in Cheshire is home to more than 100 horses and is the only racing stable to send runners to both of Wednesday's National Hunt meetings.
The decision was taken so as not to risk further spread of the disease.
Nearly 300 British-trained horses ran at last year's Festival and 82, almost one-third, made their final start between 20 and 33 days before the meeting.
Bosses at Dunstall Park announced the move to abandon the Saturday evening meeting as the probe into the outbreak was being investigated today.
The infected horses, which were vaccinated, had raced on Wednesday in Ayr and Ludlow before their cases were highlighted by the Animal Health Trust.
In severe cases, a horse might be unable to exercise for two or three months and a severe outbreak would have the potential to close down Britain's racing industry for many weeks.
In a statement, he said: "Bankhouse (his stables) follows all the available advice on disease control and all our horses are fully inoculated".
"We're very fortunate in this country that our [racehorse] population is vaccinated against equine influenza", Dunshea said, "but we're still trying to understand what particular strain of equine influenza this is".
"The disease can take up to three days before symptoms are visible, meaning it will take until Sunday at the earliest before the BHA can gather all the information required".
A further update from the BHA is expected on Monday. Declarations for Thursday would revert to the usual procedures.
It added that a plan to reschedule this weekend's key races will be constructed.
Separately, as a precaution, all of the trainers who had runners at the fixtures at Wolverhampton, Ludlow and Ayr this week have been informed that their yards have been placed under a temporary hold which means that they will not be able to make any declarations until their horses have been tested and cleared.
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