The brand increased it 2012 MAT volume by 32% after investment from brand owner the Symington family, which commissioned and released the Nielsen figures.
It achieved a 26.9% share of the UK branded port market, driven by Cockburn's Special Reserve, which grew 49% during the year.
Nielsen data also shows port bucked the trend for falling sales of fortified wine by growing 2% in volume in 2012.
“We believe that Cockburn’s will continue to grow in the UK, because it is such a well-loved brand,” said Paul Symington. “Quality, authenticity and respect for what Cockburn’s stood for, is our goal. The quality of the wine is our first and top priority, and we are delighted that the consumer and the wine trade have reacted so well to this straightforward approach."