I supply support services to primary care and social care providers, the most obvious problem is that every GP surgery, every care home and every domiciliary care organisation has to duplicate accounting tasks to satisfy rules of private sector involvement. GP surgeries who are able to deliver a service such as minor surgery have to "bid" for the contract against private sector providers, in one case the provider that won the contract couldn't deliver the service and had to approach the NHS surgery that had lost the bid, to "rent" the space and equipment to deliver the service. Time spent on this nonsense could be spent on delivering healthcare.
GP partners can get dividends if they underspend (make a profit) on their annual budget whether they are private sector or NHS, making them act like company directors when that is a job they didn't train for and often don't want to do. Those that do want to be company directors become motivated by profit not by delivering care (not their fault, that is the system they have been brought into). GP partners often buy the property that houses the surgery and rent it back to the NHS thus further enhancing their income (or pension if they retire).
All this is based on the now discredited notion that somehow competition and choice improves service, there is no evidence for this.
Care homes were privatised in the 1980's reducing the money for care by the amount of profits the private sector needs to continue their involvement. Domiciliary care is now in private hands and in order for companies to make a profit employees rarely earn more than the minimum wage. There are constant referrals to the Tribunal system to get decisions about working time and the National Minimum wage. I personally know a number of care providers who got into the business because they genuinely wanted to deliver high quality care, but in order to earn a living, they have to cut service to the bare minimum.
The conflict between health and social care places a burden on both services as patients cannot be released from hospital as the care plan is not ready, and residential homes have to upgrade to nursing as local NHS services cannot provide support to residential homes.
I could go on for ever about the bureacratic nonsense that has grown up- around Health and Social care, in the mistaken belief that somehow competition and choice improve service. And apologists for the current system will come up with examples where they believe that the private sector has led to improvements, but I have not seen any changes to health and social care that could not have been acheived more effectively by a well organised public sector, that employs excellent leadership.