However, as in so many other areas, the fungi are getting stronger and it is becoming more and more expensive to keep the Cavendish in good health - it can need as many as 15 doses of fungicidal spray. Then untold bunches end up feeding the flatfish on the Atlantic sea bed because one rotten banana ripens the rest too early.
The result is that the Cavendish is under threat. Phillip Rowe, an American banana-ologist, has had teams of technicians cross-pollinating bananas in Honduras for the past 20 years and has produced a new rival, the ominously named Goldfinger. That refers not just to its colour: Dr Rowe has a budget of $1m (£625,000) a year and is supported by the leading banana importers.
The trouble is, as Dr Rowe reluctantly admits, that while Goldfinger is a world-beating fungus-fighter and does not turn brown, taste panels have described it as "acidic" and "starchy".
But while Dr Rowe sets off on a new round of cross-pollination, Zeneca may have come to the Cavendish's rescue - and opened the way for British banana lovers to sample more exotic Asian varieties hitherto too weak to make the journey to the UK.
In collaboration with the Katholieke Universiteit at Leuven in Belgium, Zeneca scientists have found that certain plants protect their seed from fungi by generating anti-fungal proteins (AFPs). They have located the genes that produce AFPs and are transferring them to commercial crops such as oil seed rape and Cavendish bananas.
Zeneca has the patent rights for this process, and Sarah Rees, the project leader, said: "I am particularly impressed by the smooth and speedy way in which we have moved from basic research to the prospect of commercialisation."
The British company is also working with DNA Plant Technology Corporation of Oakland, California, to develop bananas with superior ripening characteristics. Bananas are grown in the tropics and harvested while still green. When they land, they are sprayed with ethylene to start the ripening process.
A Zeneca spokeswoman said: "By slowing the Cavendish's tendency to ripen, growers will be able to leave it on the plant longer, improving its flavour and nutrititional value. This will also permit the export of speciality bananas previously unsuitable for shipping."
Zeneca is concentrating on saving the Cavendish, while DNAPTC is working to develop strains previously unknown in Britain or the US, such as the Ice Cream - which has a delicious, unmistakable vanilla flavour.
But a spokesman for Geest, which with Fyffes is one of the two biggest importers into Britain, said bitterly: "We bring our bananas from the Caribbean, where the biggest threat is not fungus but hurricane." Last September, a tropical storm in the Windward Islands slashed banana output by 40 per cent.