Hundreds of patients who contracted Hepatitis C in the 1980s had to wait up to 20 years before learning of their condition, according to a lawyer.
Mr McGuire said not enough was done to trace Hep C sufferers
Frank McGuire has criticised the Scottish Blood Transfusion Service after studying documents obtained through the Freedom of Information Act.
He said the service relied on "pure chance" to find and advise patients and that some had infected their partners.
In a statement, Health Minister Andy Kerr defended the NHS staff involved.
During the 1980s doctors became aware that some patients were being infected with a new blood-borne virus. A test for what became known as Hepatitis C was developed in 1991.
From that date, the blood service could look back over previous donations and identify donors and recipients who might be at risk.
However, Mr McGuire said any effort to do so was haphazard.
He claimed a "look-back" policy was only introduced during a very short period from 1995 to 1997 but the SNBTS said it was in place from 1991. Mr McGuire also said it was wound up because of a lack of funding.
He said hundreds of patients were not told of their infection and in some cases this led to them passing the infection to their partners.
Speaking on BBC Radio's Good Morning Scotland programme, Mr McGuire said 84% of his clients said they were never called in or notified of their infection.
He said they only found out they had Hep C when they returned to hospital for a blood transfusion or for further treatment.
"My concern is they only found out by sheer coincidence and there must be a lot of people out there who don't come back to hospital who have Hep C," Mr McGuire said.
He accused the health minister of "stonewalling" new evidence and renewed his call for a public inquiry.
"What he should do is just look at the evidence, forget the politics and let's look at the people who may be infected by Hep C who don't know," said Mr McGuire.
"The other important thing is, not just the person who is Hep C, it's the person infecting other relatives who may then contract it because of toothbrushes, razors or sexual relations."
Professor Ian Franklin, medical director for the SBTS, said the "look-back" policy started in Edinburgh in 1991.
He said the testing process was "incredibly sensitive" and rejected claims Hep C sufferers were still able to give blood.
Prof Franklin said the service had a duty to tell people they had been infected with Hep C and to ensure they had access to medical care.
He defended the "robustness" of the testing and added that without having some kind of police state where you were forced to trace everybody, everything that could have been done was done at the time.
"There may be some people who received blood before 1991 who have Hep C. I don't think there are going to be many of them," he said.
"To find them would involve testing almost the whole population and I don't think anybody thinks that would be appropriate."
In a statement, Mr Kerr said he was "satisfied that the NHS staff responsible acted appropriately and in the best interests of patients".