There is almost always no difference in quality between private and NHS doctors. Indeed, you will often end up seeing the same specialist privately as you would have seen through the NHS. The difference will be when you get the appointment and how quickly you are treated, i.e. a heart bypass operation may be diagnosed for and completed in a couple of weeks with private treatment, but through the NHS this could take two or three months.
If you wish to use private healthcare, it is advisable to take out an insurance policy with a specialist health insurer, such as BUPA or PPP. Many employers also provide their workers with private health insurance, which is definitely worth finding out about if interviewing for different positions or negotiating a package.
For more information regarding expat health, insurance, health care and related issues in the UK, visit our expat health blog at ExpatHealth.org.