The 17-year-old, representing the Great Britain junior team, finished just outside of the podium places in the 1500m freestyle final after eclipsing his previous best time by 14 seconds, coming home in 15.34.
Burnell had already smashed his personal best time, to qualify for Great Britain and the event, at the British Gas Swimming Championships in March.
His next step is the European Open Water Championships in the Netherlands where he will be joined by Lincoln Vulcans' head coach Fred Furniss for his 5000m challenge at the end of this month.
"Jack should serve as a model to all as only 18 months ago he had virtually finished with swimming," said Furniss.
"He has joined us at Vulcans and worked hard, applied himself well and the combination of hard work and talent has really paid off well."