These private companies are all over England these days and I read articles in Private Eye all the time about them.
They operate on multiple sites grouped in 'hubs' which is exactly what the government originally wanted GP practices to do on a large scale to save money. That never happened mainly because it was impractical in most areas, so the next best thing was more private sector involvement.
The chances of patients seeing the same doctor are slim because doctors get sent where the need is greatest. The companies are often only meeting the minimum terms of their contract in the first place to make as much profit as possible, so it's easy for them to drop below that minimum standard when staff leave. They often have a high turnover of staff because of the way staff are treated. This includes GPs, so new GPs are very common.
When a provider is not delivering the agreed level of service, it takes ages to deal with this. Time is given to rectify and review the problem and often the end result is the company cannot provide the service it contracted to provide and moves on. This is common with any private sector contract when it is not working well, not just in the NHS. Monitoring private sector contractors must be costing us a fortune.
The NHS is selling off buildings to rent them back to the private sector, which generates income, but at the cost of an asset.
Forget about continuity of care and the NHS is definitely being privatised through the back door. Time and time again we see examples of things going wrong and it costs money to put things right. In the meantime patients and their families, and the tax payer loses out, whilst someone makes money. In all seriousness I would like to read about where privatisation of core in the NHS is working well and has been for a while.