We don’t know.
Why? Its hard to define the NHS. For e.g. do those who work at NICE work for the NHS? And what about locum, agency and part-time staff; or doctors registered but not working, or not working clinically?
So, what do we know?
In 2022, roughly 376,000 doctors were registered in the UK. This does not mean they are working, who they are working for (NHS or other, or both) or are full-time.
The age group with the highest number of doctors is among 30-34 years with nearly 60,000 professionals, followed by 58,000 doctors aged 35 to 39 years. There were nearly 14,000 doctors aged over 70 years in the UK still registered.
.. out of a total NHS workforce of about 1.2 million (and 1.5m in the UK; all figures are full-time equivalent). In other words, there are more staff who are not doctors (e.g. nurses, AHPs, managers and admin staff).
There is more information on the King’s Fund and statista websites.