Anne was the youngest daughter of high court judge Sir Malcolm Macnaghten and grew up in Northern Ireland and Kensington, London. She began her violin studies at the age of six with Hungarian soloist Jelly d'Arányi. Macnaghten later stated in an interview with The Strad that d'Arányi "wasn't really a very good teacher". At the age of seventeen she travelled to Germany to study at Leipzig Conservatory (now University of Music and Theatre Leipzig) with German pedagogue Walther Davisson, who later became the director of the conservatory.
In 1931 she co-founded the Macnaghten Concerts together with composer Elisabeth Lutyens and conductor Iris Lemare, which aimed to promote contemporary classical composers. The concert series was based at the Mercury Theatre, Notting Hill Gate and originally ran from 1931-1937.
In the same year Macnaghten founded the (then all-female) Macnaghten String Quartet, which played in many of the series' concerts. The quartet premièred works of several well-known composers as part of the concert series, including Sinfonietta, Op. 1 by Benjamin Britten in 1933, Tippet's String Quartet No. 1 in 1935 and works by Gerald Finzi, Elizabeth Maconchy and Alan Rawsthorne. The Macnaghten String Quartet are still an active quartet and regularly coach chamber music at Benslow Music Trust.
In 1952, with the help of composer Ralph Vaughan Williams (a strong supporter of the original concert series) and funding from the Arts Council of Great Britain (now Arts Council England), Macnaghten was able to revive the concert series, which was renamed the New Macnaghten Concerts and ran for over forty years, the last concert given in 1994. The New Macnaghten Concerts saw the première of works by British composers such as Harrison Birtwhistle and Richard Rodney Bennett.
The recital series saw performances by some of the most internationally renowned musicians of the era, including John Williams, Cecil Aronowitz, Peter Pears, Steve Reich, Michael Nyman, Derek Simpson, Thea King and many others.
From the late 1970s onwards, she taught violin in Hertfordshire, stopping only as a result of a fall aged ninety.
- Catherine Nelson (23 January 2001). "Obituary:Anne Macnaghten". The Guardian. The Guardian. Retrieved 30 January 2012.
- "Anne Macnaghten". The Telegraph. The Daily Telegraph. 13 February 2001. Retrieved 30 January 2012.
- "Alan Rawsthorne and the Macnaghten Concerts". Musicweb-international.com. Retrieved 2012-07-15.
- "Macnaghten Concerts (1963-75)". Arts and Humanities Research Council. Retrieved 30 January 2012.