The agency said that growth began to slow before the UK voted to leave the European Union in June, and the result "is likely to further weaken growth over the next few years".
In 2015 UK brands’ adspend grew 9.2%, and Zenith expects the growth to slow further to between 3% and 4% over the next two years.
Carat revealed its adspend report last week, and also forecast adspend to grow by 5.4% in 2016.
Zenith’s report added that the internet is "still the fastest growing medium by some distance globally. It forecasts growth at 14% a year between 2015 and 2018.
The report said: "Internet advertising accounted for 29.9% of global ad expenditure in 2015, up from 26.0% in 2014.
"By 2018 we expect internet advertising to attract 38.6% of all global advertising, after overtaking television to become the world’s largest advertising medium in 2017."
Jonathan Barnard, head of forecasting at Zenith, said: "So far the impact of the vote for Brexit has been limited, and confined to the UK.
"The global ad market has strengthened over the past few months, thanks mainly to the resilient US consumer. We expect the global ad market to strengthen further in 2017 and 2018."
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