He describes himself as a 'fourth-generation socialist'; his grandfather was involved with the Communist Party and his parents met as members of the Trotskyist Militant group.
Jones kirjeldab end neljanda põlvkonna sotsialistina – ta vedurijuhist vanavanaisa osales 1926. aasta üldstreigis, vanaisa kuulus kommunistlikku parteisse ja ta vanemad kohtusid trotskistliku grupi liikmetena.