Andrew Hawes, managing director at Mentzendorff, analysed Nielsen statistics for the category over the past 15 years before making the claim.
In 1996, port was worth £50 million in the UK, compared to £75 million in 2011.
At the same time, sherry has dropped from £124 million to £89 million.
Hawes said: “If the same long-term trend continues then port is destined to become the leading fortified wine in the UK market by 2020.”
The trend is less clear in terms of value.
In 1996, 549,000 cases of port were sold in the UK, and in 2011, this had risen to 759,000 – an increase of 38%.
At the same time, sherry has seen a decline of 42% - from 2,054,000 to 1,191,000 cases.
However, port sales reached a peak in terms of volume sales in 2004, when 895,000 cases were sold.
Since then, year-on-year volume sales have decreased every year – but not as rapidly as sherry sales.
However, Mentzendorff is confident in the future of port, and it has published a report called The Re:port outlining the way the category can grow, in association with its partner The Fladgate Partnership, which owns Taylor’s, Fonseca and Croft port houses.
In the report, Hawes notes that port enjoys “a much healthier demographic compared to other fortified wines”.
According to Nielsen, port consumers are younger on average than drinkers of other fortified wines, like sherry and vermouth.
The report states that the 25-44 age group accounts for 21% of expenditure on port, the 45-64 age group for 48% and the 65+ group for 29%.
In contrast, the 65-plus age group accounts for 55% of sherry expenditure.
Adrian Bridge, chief executive of The Fladgate Partnership, said: “Total Port volumes are likely to decline but there is plenty of scope for a growth in value.
“Consumers enjoy the taste of Port; they simply need to be reminded to buy it.
“For many Christmas would not be complete without Port – just like mince pies, carols and Christmas trees.
“It is strongly branded which is why we see strong promotional activity in the last few months of the year.
“Getting this Port promotional activity right is important to increase customer traffic.
“Importantly, though, this need not be price driven. Consumer research shows that Port is more of an impulse purchase.”