The BHA had put trainers on alert over the contagious disease after several outbreaks in northern Europe and sent out a letter to trainers recently.
The BHA released a recent statement on the dangers posed by horse flu, noting how risky this strain is.
Irish trainer Gordon Elliott ran a number of horses at Ayr on Wednesday but his runners were still travelling back home when the news of the positive tests broke and they were quickly placed in isolation away from his stables.
Meanwhile, Donald McCain has confirmed that the three cases previously detailed came from his yard in Cheshire.
Equine influenza is a highly infectious disease of horses, mules and donkeys occurring globally caused by strains of Influenza A virus.
"The fact that the cases have been identified in vaccinated horses presents a cause for significant concern over welfare and the potential spread of the disease and the action to cancel racing has been viewed as necessary in order to restrict, as far as possible, the risk of further spread of the disease", a BHA statement read.
Symptoms of EI include, high fever, coughing and nasal discharge.
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A further update on the possible continued extent of disruption is expected from the BHA - with a packed weekend of Cheltenham trials and other big races scheduled at Newbury, Warwick, Musselburgh and in Ireland.
Racing in Britain will not resume until at least Wednesday, February 13 to minimise the risk of the spread of an outbreak of equine influenza.
The authority added that a "fully informed" decision is likely to be made on Monday, allowing declarations to take place on Tuesday in time for racing on Wednesday.
McCain, who saddled Ballabriggs to win the Grand National in 2011 and has more than 100 horses in his stable, said "the BHA were contacted immediately" once the positive result for equine influenza had been confirmed and that he is "liaising closely with them about biosecurity and management of all the horses at Bankhouse". "We recommend that any trainer who has concerns about the health status of any of their horses should contact their veterinarian". It follows we would never race any horses that we could have known were infected.
In 2001, an outbreak of foot-and-mouth disease wiped out racing for two months in Britain, leading to the cancellation of the Cheltenham Festival, which is held every March.
"When new horses arrive at our yard we try as much as possible to keep them separate, but at this stage can not know if the infection came from recent arrivals or from horses returning from racing". Horses in training are required to be vaccinated for equine influenza in Ireland under the Rules of Racing.