The move has been condemned for lack of transparency by MPs and the Medical Technology Group, which represents patients, clinicians and industry.
The product councils will be made up of around 15 NHS clinicians, who will advise the DHL-run logistics service on quality issues.
The first councils are now being established for nursing and operating theatre products.
But MPs raised questions about them during a debate in the House of Commons last week (3 July).
Labour MP for Merthyr Tydfil and Rhymney Dai Havard said: 'The company running the contract seems to be choosing the people who are going to be on the product councils to do the evaluation of the evidence-based medicine. That did not appear to be a healthy, open or transparent process.'
Health minister Ben Bradshaw said he would 'reflect' on the request that there should be an ombudsman to scrutinise the purchasing and supply system.
A spokeswoman for NHS Supply Chain said: 'Many clinicians will not want it to be known that they take part [in the councils]. If they are happy for us to release the information, we will do it but we would have to seek permission first.'
The councils' discussions would concern commercially sensitive material and therefore will not be made public.
Information about the discussions will appear on a new website, the spokeswoman added, although transcripts of meetings will not be available. She added: 'Our work is governed by NHS Business Services Authority, whom we will keep fully apprised of the developments.'
John Wilkinson, a member of the Medical Technology Group and director general of the Association of British Healthcare Industries, said: 'There are critical areas of procurement that are going to reflect the range of choices clinicians will have [about the technologies they will be able to buy]. There should be a reasonable degree of transparency about how these decisions are made and this is absolutely not the case.'