He soon appeared at the Proms under such conductors as Carlo Maria Giulini, Colin Davis and John Pritchard, also becoming a frequent broadcaster at the BBC.
During a 1990 visit to England he recorded the Schumann Piano Concerto with the BBC Philharmonic Orchestra and gave a recital of works by Ernő Dohnányi and himself.
During the same year Rajna played the solo piano part in the first, and so far the only South African performance of Messiaen's monumental Turangalîla-Symphonie with the Cape Town Symphony Orchestra.
The former Foundation for the Creative Arts commissioned these works as well as the Rhapsody for Clarinet and Orchestra (1995), premièred by Robert Pickup, the NSO and Richard Cock in 1996.
The same year Rajna wrote Tarantulla for violin and piano in response to a commission for the 2002 Pretoria contest by the University of South Africa (Unisa) International String Competition.
Rajna's recordings of the complete piano works of Spanish composer Enrique Granados (1867-1916), made in London for CRD in 1976, were reissued in 2004 on six CDs in a box set and distributed worldwide by Brilliant Classics.
The premiere took place at the Spier Summer Arts Festival, Stellenbosch, in March 2005 and in 2007 the opera was revived at the Klein Karoo National Arts Festival in Oudtshoorn, where it gained prizes in two categories: best musical show and most promising newcomer (Golda Schultz, soprano, the opera's leading lady).
In 2006 he completed The Creation-A Negro Sermon for chorus and orchestra, written for the First Cape Town International Summer Music Festival in 2006.
In response to a commission by Unisa to write a set piece for the new Grade 7 Piano Examination Album he completed his Oriental Feast in August 2006.
Rajna prepared and reissued on his label a series of his landmark recordings of earlier vintage, now digitally remastered and available on CD for the first time.
He released Brahms's B flat major and Schumann's A minor piano concertos, Liszt's Transcendental Studies coupled with their earliest version, the 12 Etudes, Op.