Anyone able to shed light on this, on that beach strip and perhaps the aircraft used?
Or maybe it wasn't Ibiza, Menorca or some other island perhaps?
It wouldn't have been Menorca. The 'old' aerodrome at San Luis was in use from 1947-69 as the island's airport, then operations moved to the new 'Mahon' airport at San Clemente and the Real Aero Club de Mahon took over San Luis aerodrome.
The new airport used to be a delightful little place - you could sit outside with a pallofa on the terrace bar right next to the apron waiting for friends to arrive. But now it has been extended and expanded and has lost all its charm, I gather.
Iberia started operating the Caravelle in 1962; however, by then Es Codolá airport had been upgraded with a tarmac runway.
Between 1958 and 1960, the 'small noisy aeroplane' which used to operate between Barcelona and the dusty airstrip at Ibiza was probably the Bristol 170 operated by Aviaco:
Or perhaps an Iberia DC-3; services from Ibiza to Barcelona and Valencia also started in 1958.
Jet aircraft started flying direct to Ibiza following runway extension in 1962.