Swinburn was born in Oxford. He was the son of Wally Swinburn, who won the Irish flat racing Champion Jockey title in 1976 and 1977 and was the first jockey to record over 100 winners in an Irish flat season. Nicknamed the "Choirboy", he rode his first winner, Paddy's Luck, on 12 July 1978 at Kempton Park but gained considerable fame for riding the superstar Shergar to victory in the Epsom Derby in 1981 by a record 10 lengths. Swinburn went on to win the Derby two more times.
After retiring as a winner of numerous Group One races, including eight British Classics, Swinburn began working as a licensed trainer in 2004 and operated Walter Swinburn Racing Stables based at Church Farm in Aldbury, Tring, Hertfordshire. At the end of the 2011 UK Flat Season Walter Swinburn gave up his flat training licence.
Peter [Harris] has been taking a step back and I was here as a salaried trainer. The dispersal sale of his bloodstock last year was the start of it, and he'd made it known that he would continue funding the operation only until October 31 and thereafter it was up to me to fund it myself if I wanted to carry on here. With a big yard like this you need the boxes full up, and Peter is the main owner. To suddenly find you are minus 50 horses would not have been a good starting point, and a big decision had to be made... I'm very confident you haven't seen the last of me as a trainer, but the advice from the accountants...was that it (training at the yard) wasn't viable at the moment
Swinburn married Alison Harris, the daughter of Peter Harris, a retired horse trainer, entrepreneur and multimillionaire in 2002. They had two daughters, Claudia and Millie. His family home was Stocks House at Aldbury, a golf spa hotel and resort purchased by Harris in 2004 and converted for domestic use.
Swinburn died in London on 12 December 2016 at the age of 55. An inquest in January 2017 heard that Swinburn had fallen from a bathroom window, and the coroner ruled his death an accident.