Peters was born in Middlesbrough and brought up on the council estates. His father worked on Tees Dock as a stevedore and his mother worked as an insurance agent. He was the middle child of three boys. He attended Grammar school having passed the scholarship entrance exams. He was not academically inclined and by self-admission would pass each academic hurdle throughout his entire career by achieving only what was necessary. He achieved eight ordinary levels and then took four Advanced level subjects in Mathematics, Physics, Chemistry and Biology; the first pupil at his school to take four ‘A’ level subjects.
After leaving school he went to Stirling University to study Mathematics and then went on to take a Post Graduate Certificate of Education at Sheffield University, where he gained a distinction in teaching practice. He taught mathematics for several years in secondary schools and colleges. During his teaching career he undertook extensive voluntary work that spanned across organisations such as ‘Help the Aged’, the NSPCC (working with educationally and socially disadvantaged children), the RSPCA and he also took classes at North Sea Camp for young offenders alongside work in the probation service. Peters’ interest in the support for victims of crime led him to help start a victim support scheme in his town of Boston. This movement spread and resulted in the National Victims Support Scheme.
Peters re-entered University to study medicine at St Mary’s Medical School, part of the University of London. During his time as an undergraduate he was the year representative in his first year, the Secretary of the students Union in his second year and became President in his third year. He won the prize for medical statistics. Whilst at St Mary’s he also directed the medical school opera and became the president of London University Athletics. He represented London University at the British University Championships where he made the final in the 200 metres. Peters was awarded colours for outstanding service to the University of London.
After graduating as a doctor he undertook several positions within hospitals and institutions across the UK in disciplines of surgery, medicine, general practice and various branches of psychiatry. He gained his membership exams for the Royal College of Psychiatrists and became a Consultant psychiatrist within the National Health Service, where he worked for twenty years. During this time he became the Clinical Director of Bassetlaw District General Hospital alongside his commitment to patient care. His career within the National Health Service culminated in working at the Special Hospital at Rampton under the Home Office working with patients with dangerous personality disorders. The press named him as being involved with the detection and solving of the Soams murders.* Peters specialised for some time in the treatment of alcohol and drug disorders and was a member of the Medical Council on Alcohol.
In parallel to his hospital clinical work he worked at Sheffield University as a Senior Clinical Lecturer in medicine where he became Undergraduate Dean and Professor of Psychiatry (positions which he still currently holds as of 2015). During his time at the University he gained a master's degree in Medical Education, a Post-Graduate Diploma in Sports Medicine and was awarded a Doctorate in Medicine. Peters set a precedent by being bestowed the Senate award for teaching excellence on two occasions, still a unique achievement, and represented the University at a meeting to celebrate teaching excellence at Downing street. Peters set up the mentoring system for student support within the medical school and led on this for several years.
In 2001 a former student at Sheffield recommended Peters to the British Cycling team, and he moved from part-time to full-time work with the team in 2005. Particular Olympic cyclists he helped include Chris Hoy and Victoria Pendleton. Sir Dave Brailsford has described Peters as "the best appointment I've ever made." Peters stepped down from his role with British Cycling in April 2014 when Brailsford left his position as Performance Director.
Peters worked very successfully with Ronnie O'Sullivan, helping him win his 4th and 5th World Snooker titles in 2012 and 2013 respectively. Ronnie also personally thanked Peters following his victory in the 2017 Masters final.
After the 2012 Olympics Peters was appointed by UK Athletics to work with the country's high performance athletes. Sprinter Adam Gemili, who won gold at the 2014 European Athletics Championships in the 200 metres and silver at the 2014 Commonwealth Games in the 100 metres, attributed his ability to perform under pressure at major championships to his work with Peters.
From November 2012 Peters has worked with Liverpool F.C.. In March 2014 he was recruited to help the England National Football Team.
In later life Peters has competed in athletics and has held multiple World Masters Champion Titles and World Records over the 100, 200 and 400 metres.
Peters has talked about happiness, and quality of life, as key life goals.