Bupa is seeking at least a 15% reduction in major hospital group fees following the Competition and Market Authority's (CMA) final remedies on private healthcare.
Speaking at the British Medical Association's Private Practice Conference, Dr Damien Marmion, managing director of Bupa Health Funding, said this would drive "better value" for customers.
Dr Marmion said: "It (the CMA) has made it clear that hospitals have been making excessive profits at the expense of customers. It is an absolute priority of ours to address this - and to secure the agreement of current and future private hospital owners for significantly lower fees."
He confirmed that while the amount would vary by hospital group, Bupa were aiming for a reduction of 15% or more.
Marmion's comments were made in response to the CMA's final report on the private healthcare market.
This was the result of a two-year investigation by the Competition Commission (CC), which became part of the new Competition and Markets Authority (CMA.)
It found that many private hospitals face little competition and that there are high barriers to entry. This leads to higher prices for self-pay patients in many local areas - and for both self-pay and insured patients in central London.
Remedies included a crackdown on consultant incentive schemes and a push to increase availability of consultant fees and the performance of consultants and private hospitals.
Hospital network HCA was also required to sell the London Bridge and Princess Grace hospitals or alternatively the Wellington hospital including the Wellington Hospital Platinum Medical Centre (PMC).
However, while Dr Marmion welcomed the CMA's proposals as a step in the right direction, he stressed the sector "must still go further."
He added:"Let me be very clear on this: where the CMA has found that a major hospital group has been charging rates that are excessive, Bupa will be seeking a significant reduction from them.
"The amount will vary by hospital group, but in some cases we will be aiming for a reduction of 15% or more. We will use these reductions to give hard-pressed customers better value from private healthcare and to grow the market, for the benefit of all participants in the market."
Marmion also reitirirated that any savings made as a result would be passed onto Bupa's customers, to help attract more people into private healthcare.
Fellow insurers AXA PPP, Simplyhealthh and Aviva also recently promised to pass cost savings onto their customers.
Marmion added:"The proposed reforms will, however, take time to implement - even if they are not appealed, and I don't think even the most enthusiastic advocate for them would hold that they are a panacea for the challenges facing our sector."
