By the mid 1960s, Eric Pinkett – supported by the patronage of Sir Michael Tippett – had managed to put the LSSO on the UK musical map.
The orchestra also established an international reputation due to its regular concert tours of major European cities, an annual tradition that started with visits to Essen in 1953, The Hague in 1954, Aarhus in 1955 and Oslo in 1956.
Over the years the orchestra's repertoire has included a number of specially commissioned works by composers such as Michael Tippett (The Shires Suite), David Bedford (Alleluia Timpanis), Bryan Kelly (Sancho Panza, Sinfonia Concertante), Anthony Milner (Te Deum), Alan Ridout (Concertante Music, Symphony No.2, Funeral Games for a Greek Warrior), Brian Bonsor (The Pied Piper of Hamelin), William Mathias (Sinfonietta), Herbert Baumann (Variations on an Old English Folk Song), and Herbert Chappell (Overture Panache).
Since the late 1950s, many illustrious musicians have conducted the orchestra and these have included Michael Tippett, Alan Ridout, Arthur Bliss, Adrian Boult, Malcolm Arnold, Charles Groves, Norman Del Mar, George Weldon, Rudolf Schwarz, James Loughran, László Heltay, Herbert Chappell, Bryan Kelly, Alan Ridout, Herbert Baumann, Douglas Cameron, Lesley Woodgate, Stanford Robinson, Oivin Fjelstad, Bernard Keeffe, Alexander Goehr, Russell Burgess, Uri Segal, Havelock Nelson, Willy Gohl, Dan Vogel, Maurice Handford, Pierre Cao, Myung-whun Chung, Douglas Young, William Mathias, Martyn Brabbins, Stuart Johnson and André Previn.
In a press review of one of the concerts given by the orchestra during their 1969 tour of Germany with Sir Michael Tippett and Richard Rodney Bennett, the LSSO was hailed as "Britain's best cultural export".