And some parents are being unduly pressurised to give their consent, it is claimed.
But research in The Lancet medical journal found that a slim majority of parents in nine European countries, including the UK, had not fully given their consent.
The researchers discovered that 42 parents out of a sample of 200 did not fully understand the procedure or treatment and 43 had simply not been given enough information.
In a further 21 cases, there was a question mark over whether parents had been pressured into signing the consent form.
The study is released just a day after the publication of a British Medical Association book giving guidance to doctors on the dos and don'ts of obtaining consent from patients.
It says young children should be helped to express their views about medical treatment as soon as they can talk, and that parents who insist on hiding medical details from their children should be discouraged from lying.
The BMA guidance also advises doctors how to decide whether patients are mentally competent to give consent, and on the impact of the recently-introduced Human Rights Act.
Beefed up process
Only 5% of doctors questioned had been given some form of training about the right way of seeking consent.
The investigators suggest that the consenting process could be beefed up by making sure all staff, including researchers, receive guidance on how to do it.
In addition, parents should be given written material about operations or treatments.
Ms Suzette Woodward, assistant director of clinical governance at Great Ormond Street Children's Hospital in London, has carried out her own investigation into the quality of consenting.
She found that the majority of parents were satisfied with what they were told, but thought this might be the result of a good result in the subsequent operation.
Closer analysis found that a third of parents wanted more information about the potential risks or complications.
She told BBC News Online: "I think strongly that even if they are told about the risks, they are not absorbing it.
"It needs to be explained in a way that they can remember it.
"I think doctors and nurses need to be trained at a very junior level. At the moment they learn from osmosis which is a shame."
The issue of consent figures strongly in the inquiry into the retention of organs from children who died at Alder Hey Hospital in Liverpool.
Parents claimed they had not been properly informed that organs could be kept for research.
A report into the affair is expected early in the New Year.