The Stirlingshire-based firm, which is run by the original founder's children and grandchildren, has upped its share of the block butter market to 10.9 per cent for the 24 weeks up to June 23, compared to 9.8 per cent for its Danish rival.
This follows a steady rise in sales ever since Graham's introduced block butter in 2005 but last year marked the biggest upturn yet, according to the research from the Kantar World Panel.
Graham's attributed the sales jump to a growing number of consumers wishing to "buy Scottish" and the firm's existing milk customers who are extending their brand loyalty.
Carol Graham, marketing director of Graham's, said: "This is a landmark time for our business and we will continue to work hard to engage with shoppers and develop our brand strength so that more and more people consider making the switch to Graham's."
The firm recently secured a £20 million funding injection from Royal Bank of Scotland and its asset finance arm Lombard to invest more in its cream and butter ranges, as well as enhance its brand south of the border.
Managing director Robert Graham has previously announced his intention to break the £100m sales barrier after unveiling sales of £68m in the year up to March 2013, up from £56m in the preceding 12 months.
The dairy has seen sales grow by about 20 per cent for the past 15 years.
Butter consumption has risen by 10.9 per cent across the UK over the last decade.