Her debut at London’s Wigmore Hall in 1974 was followed by concerts and broadcasts in the UK and tours worldwide, both as solo recitalist and concerto soloist.
"[5] Beginning in 1975, Thwaites has made a point of including music by Australian composers such as Malcolm Williamson, Margaret Sutherland, Arthur Benjamin, Peggy Glanville-Hicks, Jennifer Fowler, Alison Bauld, David Worrall, and many more, whether in solo recitals, concertos and chamber works.
Most notably, Penelope is a featured solo, chamber and orchestral artist on eight of Chandos Records' 21-CD Grainger Edition (re-issued in 2021).
BBC Music Magazine (February 2017) commented "passion undimmed, along with dexterity, the playing’s flair and precision are unchanged...Listening again only makes the heart grow fonder...I can't think of another composer who so quickly and quirkily enhances life.
(based on an incident in the life of John Wesley) premiered at the Westminster Theatre in London's West End, following a nationwide tour.
[13] The musical has had more than 40 productions since then – both amateur and professional - and a concert version was recorded in 1999 on the SOMM label, starring the legendary actor, Keith Michell.
[14] In 2020, SOMM recordings released "From Five Continents", a CD of twenty-four of Penelope's choral works and songs, with Ex Cathedra under Jeffrey Skidmore and soloists Carolyn Sampson, James Gilchrist and William Dazeley.