The Dublin-born swimmer represented the Isle of Man during her career and won her last title in 1968.
Jackson was the first Manx woman to win a Commonwealth Games medal, taking bronze in the 200m freestyle in 1970, and competed at the Mexico Olympics.
Isle of Man Swimming manager Leonie Cooil said Atkinson’s triumph is a “fantastic achievement which provides a real boost for Manx swimming”.
She added: “To be our first British champion for than half a century is a very special achievement. It’s a piece of history and she is the first-ever Manx-born champion.”
National Swimming coach Lee Holland added: “We always knew she had the potential and she has really worked on all aspects of her racing.
“We couldn’t be more proud of her achievements – it will be like the (Mark) Cavendish effect and inspire all our young swimmers.”
Atkinson is the reigning Isle of Man sportswoman of the year.
