Leslie Thompson, 79, who suffers from lung cancer, underwent the procedure – called a percutaneous cervical cordotomy – at St James’s University Hospital.
The procedure involves using a radiofrequency generator and needles, which heat up and burn the nerves on the opposite side of the neck to where the pain is located.
Patients are still able to walk and move around freely after having undergone the procedure.
A spokesperson said: “It is only suitable for patients who have one-sided pain and are well enough to benefit from the procedure.”
Following the procedure, Mr Thompson said: “They look after you really well here.
“I feel less pain in my lung.
“I think it’s a good idea and it will help a lot of other people.
“The pain you get with cancer is unbelievable and it affects lots of people.”
Leeds is only the fourth UK centre to offer this procedure, after London, Glasgow, and Liverpool.
Dr Sheila Black, consultant in anaesthesia and pain management at Leeds Teaching Hospitals NHS Trust, carried out the procedure after training at hospitals in Glasgow and London.