Andrew Nicholson has undergone successful surgery to repair the injury to his neck suffered during a fall from his mount Cillnabradden Evo at the Festival of British Eventing on the weekend.
In a message delivered via his family, the operation is described as having gone "well and his condition is stable. Andrew is comfortable and has full range of movement. His family would like to thank the many well-wishers".
Nicholson fell after the last fence on the cross-country course, where he was in the lead.
He was taken about an hour's drive to John Radcliffe Hospital for treatment.
The hospital is listed by Britain's National Health Service as "Oxfordshire's main accident and emergency site and provides acute medical and surgical services, trauma and intensive care".
The 54-years-old's pursuit of selection for a New Zealand record eighth Olympic Games will be in jeopardy but, at such potentially pivotal moments in one's life, such matters are trivial compared to maintaining wider health.