Apart from singing, Murphy played piano and church organ. Following graduation, he moved to London to pursue a singing career and supported himself with a job as a school master. Hearing about a BBC television series, Music for You, he contacted the office of its presenter, conductor and producer, Eric Robinson who gave him an audition for the chorus, then offered him solo spots in the series. During the series, Murphy sang with notable performers, including Italian opera singer Benamino Gigli and Robert Helpmann. In 1957, Murphy was given a recording contract by George Martin of Parlophone Records, and Murphy turned to singing big pop ballads. In the same year he married Patricia. In 1960 Murphy went to the US to guest on the Arthur Godfrey show and toured the North America in 1961. During this visit, Murphy guested on Rick Campbell's Better Late Show and on the Elwood Glover show on CBC.
Ireland
He returned to Dublin when Ireland announced its own state television service. Murphy auditioned for RTÉ television and became presenter of its first chat show, Visitors Book. He also became a producer/director, directing news and producing a weekly music show, Just For You. Oriole Records label offered him a recording contract but changed his name to Mark Dwayne. With this label he had hits with "Remember Me Huh!" and "Little Bitty Heart". To promote these records he starred on ABC Television's Thank Your Lucky Stars in the UK, which rivalled the BBC's Top of the Pops.
Abroad
Murphy then took up offers from UK television stationsWestward Television and Southern Television which covered the south west and south of England, as anchorman on their respective nightly magazine programmes Westward Diary and Day by Day. At Westward he presented with Desmond Wilcox a major documentary on the Tolpuddle Martyrs. Once more Murphy moved to Manchester as anchor on BBC's nightly news magazine Look North which then covered the whole of the north of England. Before joining Westward, Murphy had guested as a singer on ATV television's series Music Shop with Shirley Bassey. In the late sixties record producer Denis Preston invited him to come up with a concept for an album of Irish songs which resulted in A Nation Once Again, each song representing a period of Irish history. In 1967, President of IrelandÉamon de Valera received Murphy in a half-hour private audience in which he congratulated him for being such a good unofficial ambassador for his country. Following a concert appearance with comedian Dave Allen at London's Royal Albert Hall, Murphy starred on BBC television's series Dee Time presented by Simon Dee. In this series he appeared with Engelbert Humperdinck, guitarist Jimi Hendrix and folk artist Donovan. In 1974 he joined Liverpool, Radio City as their first presenter on air with The Breakfast Show. He also hosted programmes like Midday with Murphy and Downtown. He stayed for nearly 3 years but now, with a second son, felt it was more important to spend quality time with his family.
Ireland
Back permanently in Dublin he continued presenting and producing sponsored programmes for clients such as Coca-Cola and Johnson Wax as well as presenting programmes for RTÉ's new station, RTÉ Radio 2. Then in 1982 RTÉ offered him a 10-minute weekly filler slot titled Mailbag for 3 weeks. The programme which dealt with viewers letters concerning programmes was extended to 6 weeks. Before the year was out it had become a half-hour show going out on both of RTÉ's television channels. Finally it ended 14 years later. However, Murphy continued to use the Mailbag concept into the 2010s, complete with postmodern ironic touch, with his regular "E-mail Bag" segments on Today FM radio's The Ray D'Arcy Show. In early 2015 Arthur moved with Ray D'Arcy's team to RTÉ and he continued to present the weekly mailbag slot in the afternoon on RTÉ Radio 1. Murphy lived in Dublin with his wife Patricia up until her death on 2 April 2016. He enjoyed pursuing various interests both in broadcasting and in other fields. He received an enquiry from an Englishman asking if he was descended from the 18th century Irish writer actor, playwright, journalist and barrister Arthur Murphy, a famous man in his time. Perhaps the enquirer thought that Arthur was this Arthur. Much as he would have liked to say "yes", the answer was in the negative.
Death
Arthur Murphy's death was announced by RTÉ News on 8 February 2019, he was 90-years-old.