But while working as a senior house officer in intensive care, he witnessed an operation to correct an aneurysm [bulging blood vessel] in the brain, and was "smitten" by neurosurgery.
Another possible influence on his choice of specialisation was the diagnosis of a brain tumour in his then three-month-old son William. Successful surgery ensured a complete recovery. Marsh also has two daughters, Sarah and Katharine, from his first marriage. He is now married to social anthropologist Kate Fox, acclaimed author of the Watching the English.
William's illness is also relevant to the way he practises medicine, trying to find the balance between being "kind and detached". He remembers being simultaneously anxious and very angry when William was ill. "Doctors and nurses tend to be fit young people. When you cross over into being a patient or relation of one, you realise how little you understand of that experience. I would like to think it made me a better doctor."
Neurosurgery, appropriately, seems to be an especially cerebral type of medicine. As he explores in the book at length, Marsh explains that what is particular about dealing with tumours and aneurysms is that good decision-making can be just as important as an ability with a scalpel.
"It's not just life and death issues; surgical mortality rates can't be applied to neurosurgery, because sometimes death is the best outcome, certainly better than being left with severe disability. And we see so much disability in neurosurgical patients."
He recalls cases which "went bad" and talks in the book of the "many disasters and unexpected tragedies" he has witnessed. Of one patient, whose life was saved by the removal of a pineal gland tumour, he writes: "I knew that as time went by the grief I felt at what I had done to the young woman would fade. The memory of her lying in the hospital bed, with a paralysed arm and leg, would become a scar rather than a painful wound. She would be added to that list of my disasters - another headstone in that cemetery which the French surgeon Leriche once said all surgeons carry within themselves."
The book makes for gripping, uneasy reading: "In this age of increasing expectations and consumerism," he explains, "the public need to know and understand that medicine is dangerous and uncertain; they need to be educated. If they want to be treated like children, placing themselves in the hands of God-like doctors fine, but they then can't complain afterwards. Patients need to accept things can go wrong and be grown up about it.
"It is not like taking your car to a garage, outcomes after surgery are often very uncertain; patients are right to be anxious - I still get tense before operating. I'm told when I was younger I used to throw chairs around - I don't do that now. My main responsibility is training the juniors."
He also operates at the Lipska Street Hospital in Kiev, Ukraine, where he has been volunteering for 20 years. Next year, he will visit Nepal to work, stepping back from full time in the NHS, as he approaches retirement.
"I'm getting more sympathetic with age," he says. "You get impatient with older patients when you are younger, but now I feel terribly sorry for those with brain degeneration. I think, in 10-20 years that could be me." He takes very seriously measures that can possibly prevent dementia. "I run every day, including a sprint which leaves me breathless; I do press-ups and chin lifts, and I cycle everywhere."
He remains fascinated by the brain. "Working with it teaches you about suffering, and the unpredictability of life, that the more we know about the brain, the more we realise we don't understand. We are still scratching the surface."