Had the Montreal Protocol not existed, the ozone hole would have become 40% bigger by 2013, a study has found.
The Montreal Protocol came into force in 1987 in response to the use of ozone-depleting substances like CFCs that were commonly found in things like fridges and aerosols.
Following the agreement, atmospheric concentrations of these substances continued to rise until the peak in 1993. Since then they have declined and the ozone layer has been recovering.
Scientists from the University of Leeds have now looked at what the ozone layer would have looked like without the Montreal Protocol by using a high-tech computer model of atmospheric chemistry.
The study, published in the journal Nature Communications, showed how the hole over the Antarctic would have grown in size by an additional 40% by 2013.
Study lead author Martyn Chipperfield said: "Ozone depletion in the polar regions depends on meteorology, especially the occurrence of cold temperatures at about 20km altitude – colder temperatures cause more loss.
"Other studies which have assessed the importance of the Montreal Protocol have used models to predict atmospheric winds and temperatures and have looked a few decades into the future. The predictions of winds and temperatures in these models are uncertain, and probably underestimate the extent of cold winters.
"We have used actual observed meteorological conditions for the past few decades. This gives a more accurate simulation of the conditions for polar ozone loss."
As well as growing, the findings showed the layer would have become significantly thinner over other parts of the globe. Declines over northern hemisphere middle latitudes would have more than doubled by 2013, with the losses leading to increases in surface ultraviolet.
In Australia and New Zealand, surface UV would have increased by between eight and 12%, while the UK would have seen an increase of 14%, which would have led to more skin cancer cases.
Chipperfield said: "Our research confirms the importance of the Montreal Protocol and shows that we have already had real benefits. We knew that it would save us from large ozone loss 'in the future', but in fact we are already past the point when things would have become noticeably worse."