Dr McMinn, of Clent, near Stourbridge, is being investigated over claims he kept the bones of more than 5,000 patients he operated on at Edgbaston Hospital in Birmingham.
But former patients who underwent pioneering hip resurfacing treatment have continued to rally round the under-fire surgeon.
BMI Healthcare, which runs the hospital, has set up a helpline for patients potentially affected but Hannah Travis, a senior solicitor at Bolt Burdon Kemp, said the firm has a responsibility to reach out to patients, rather than the other way round.
It's alleged Dr McMinn collected bone and tissue samples from patients without permission over 25 years.
Circle Health Group, which acquired BMI Healthcare in June this year, said the hospital is now under new leadership and that it was taking the issues “incredibly seriously”.
Several former patients have contacted the Express & Star in support of Dr McMinn, stating his groundbreaking procedure, which was used on tennis legend Sir Andy Murray, helped them maintain a normal way of life.
Solicitor Ms Travis said: "BMI healthcare have now set up a helpline for Mr McMinn’s former patients but they had not initially contacted anyone who may have been affected which is disgraceful. BMI need to ensure they are proactively investigating and then contacting any patients affected as soon as possible rather than expecting and relying on thousands of understandably panicked patients to make contact with them."
Former patient Harry Hardman, of Warley, who was treated by Dr McMinn in the early 90s, said he was not concerned at all by the claims.
"I'm now 77 and still walking around on that hip. What he did with the bit of bone that came out I couldn't give a monkeys," he said.
"If a car breaks down you take the piston out, have a look at it, how you build it, how you make it better.
"I would not have had the active life I had without Mr McMinn's intervention. I will be eternally grateful to him."
Gordon Starkey, 79, from Kingswinford, had both hips resurfaced in 2002.
He said: "I have no qualms with what he did for me. I'm assuming he wanted the bones for research.
"It didn't alarm me. What would have happened to the bones anyway? Would they be disposed of?"