29 March 1998
On 29 March 1998, British Airways (BA) prohibited smoking on all flights. Other countries across the world had begun to impose the first restrictions on smoking in public in the 1970s, but legislation was only applied to airlines during the 1980s. Initially airline companies were made to separate smoking areas from non-smoking areas on planes, but by the late 1980s all smoking was prohibited on all flights of less than two hours.   However, as this entry indicates, smoking was only prohibited on all flights (international and domestic) a decade later. Local airline South African Airways (SAA) prohibited smoking on all flights soon after BA.   
References

Wallis, F. (2000). Nuusdagboek: feite en fratse oor 1000 jaar, Kaapstad: Human & Rousseau.|Help with Smoking, 'The History of Smoking-how and why smoking began and has risen dramatically' [online], Available at www.helpwithsmoking.com [Accessed: 28 March 2014]