Boughton was born in Birmingham, U.K., on December 18, 1948. His grandfather Rutland Boughton was a noted composer, and both his parents were musicians. He started out as a cellist, studying at London's Guildhall School of Music, the Prague Academy of Music, and the New England Conservatory in Boston. He played cello in several British ensembles, but his interest shifted to conducting. In 1980, he founded the English String Orchestra in the city of Malvern; later, as the group began to play repertory for larger ensembles, it was renamed the English Symphony Orchestra and moved to Worcester. Boughton commissioned new works from many top British composers during his tenure and led the orchestra in an acclaimed series of recordings for the Nimbus label. In Malvern, Boughton became artistic director of the Malvern Festival in 1983, collaborating with composer Michael Tippett in 1985 on a celebration of Tippett's 80th birthday.
In 1986, Boughton became conductor of the Jyväskylä Symphony Orchestra in Finland, holding that post until 1993 and increasing the orchestra's audiences by some 60 percent with programming that mixed familiar works by Sibelius with new music. Boughton returned to Malvern in 1996 and again championed contemporary music in the festival's programming, organizing a celebration of composer Nicholas Maw's 60th birthday in 1995. Boughton continued to conduct the English Symphony Orchestra until the 2005-2006 season, offering a complete cycle of Beethoven's symphonies in his last year. From 2002 to 2008, he was artistic director of the Nimbus Foundation; in that capacity he created a new summer concert series at the nearby Wyastone Estate in Ganarew. In the summer of 2007, Boughton returned to the U.S. to take the post of music director and conductor of the New Haven Symphony Orchestra. He has continued to champion new music, beginning a new composer-in-residence program with Augusta Read Thomas as the first resident, and he received an ASCAP award for adventurous programming in 2011. With the orchestra, he also began a project to record the works of English composer William Walton. Boughton has also taught at Yale University in New Haven and has conducted the university's orchestra.
In Britain, Boughton has made several recordings for the Lyrita label with the BBC National Orchestra of Wales. In 2018, he led the orchestra in an album of works by Scottish-American composer Thea Musgrave, celebrating her 90th birthday. He is also founder and chair of Connecticut's Guilford Performing Arts Festival., Rovi