Questions have been tabled in the House of Lords' asking the government for its assessment of key elements of the private medical insurance (PMI) market.
They query the validity of using open referrals and the exclusion of clients' pre-existing conditions and their impacts ‘on healthcare in the United Kingdom'.
However the process has been defended by Bupa, which said patients approved of the measure.
Lord Walton of Detchant, former chairman of the General Medical Council (GMC), who tabled the two parliamentary questions in the House of Lords, has previously raised concerns about insurers' fixed fee schedules and data for consultants.
His first question asked whether the Government has assessed "restrictions placed by Bupa and other private medical insurers on the choice of consultant or hospital to which insured patients can be referred, irrespective of the advice of their general practitioner, and their impact on healthcare in the United Kingdom".
While the second queried what assessment the government has made of "the degree to which Bupa and other private medical insurers exclude pre-existing conditions from their cover, and its impact on healthcare in the United Kingdom".
A statement from the Federation of Independent Practitioner Organisations (FIPO) which has publicly criticised much of Bupa and the PMI market's operation, suggested that submissions to the Office of Fair Trading's (OFT) review of the private healthcare market contradicted insurers views around open referrals.
"PMI providers indicated to the OFT that they did not possess sufficiently detailed information on the quality of care offered by consultants recognised by them and were in most instances unable to advise patients beyond information relating to the consultant speciality and location," it said.
Geoffrey Glazer, chairman of FIPO, added: "BUPA has made several claims about the variation in clinical practice between specialists, but has never been able to produce hard data to support the contention that this leads to better outcomes.
"The implication that the ‘Bupa approved consultant' is of a higher quality is entirely unsubstantiated.
"In fact, only those consultants who have agreed to Bupa's scale of fees will be on the list of approved consultants, thereby actually restricting patient choice.
"Patients should not have to throw away their choice of consultant, have the opinions of their GP discarded, or be restricted by the exclusion of pre-existing conditions in their cover in this fashion," he concluded.
However Bupa defended its stance and said it had the backing of its patients in the matter.
"Our members have increasingly been asking us to help them to choose their consultant because of the lack of good quality information about quality and outcomes of consultants and hospitals," Dr Natalie-Jane Macdonald, managing director of Bupa Health and Wellbeing said.
"This can result in members receiving a shortfall for the service they receive, which can be particularly frustrating for them at a time when they are focusing on getting better.
"Some of the problems faced by our members were also raised in the recent (OFT) market study, which highlighted that many GPs refer their patients to consultants without any objective quality data, or information about whether a consultant will unexpectedly charge the patient more than their health insurance will cover.
"The OFT's research showed that the most common information sources GPs use when referring private patients are hospital marketing literature and informal social contacts.
"Our Open Referral Service aims to increase patient choice, giving our members control and enabling them to make informed decisions about their healthcare and we have found that demand from our members is extremely strong," she added.
The insurer also noted that since December 2010 it had provided the open referral service to over 50,000 patients, with its latest customer research, conducted at the end of 2011, showing a 54% higher rating for customer satisfaction and a 21% higher rating for quality of service.
