The patients were infected by an HIV-positive donor whose contaminated blood escaped detection. One has since died of a condition unrelated to HIV. The others have been identified and offered counselling and support.
It is the first case of HIV infection in England since screening for the virus was introduced in 1985.
All blood donations are tested but there is a window of 20 to 30 days after infection before the virus can be detected.
The disclosure is a blow to the blood service which has suffered repeated shortages and is urgently seeking new donors.
Two years ago a batch of faulty blood bags resulted in two patients contracting septicaemia from infected blood. Hospitals use 10,000 units a day and demand is rising as more patients undergo surgery.
Angela Robinson, medical director of the service, said the case was tragic but extremely rare, the first in over 30 million donations made since 1985, although there was a similar case in Scotland in 1986. "No one else is at risk. Patients can be reassured that blood transfusion in this country is among the safest in the world," she said.
A single donation of the infected blood was made in the north-west of England last summer and divided into red cells, plasma and platelets, which were given separately to the three patients.
Because the donor had only been recently infected, the virus did not show up in routine testing but was still capable of being passed on.
The case came to light last month after one of the patients was found to be HIV-positive while undergoing further hospital treatment. Doctors traced all the blood donations the patient had received, and a special sensitive test, known as a PCR test, which detects the presence of antibodies, was carried out on the original sample taken from the donor. This revealed the presence of the virus. All samples taken from donors at the time they give blood are kept routinely for two years in case such backdated checks have to be made.
Donors are given a questionnaire about their lifestyle and sexual habits which the National Blood Service said should have eliminated anyone at risk of carrying the infection.
They are told they should never give blood if they are a man who has had sex with another man, injected drugs or worked as a prostitute. They should not give blood for a year after sex with a prostitute or after injecting drugs or for anyone of any race who has been sexually active in Africa.
A spokeswoman for the service said that the infected donor had been traced. "Either the donor did not know they were infected or they lied," she said.
Heat treatment is used to eliminate viruses present in blood products such as Factor VIII for haemophiliacs, but it cannot be used on whole blood because it would destroy it.
The spokeswoman said the more sensitive test for HIV, which is known as polymerase chain reaction (PCR), was not suitable for screening individual donations. She said the service had no plans to review its procedures.