Proud went under 46 seconds for the first time, beating his own record in the men's 4x100m freestyle with 45.97.
Aimee Willmott won her fourth medal with 400m individual medley gold.
Lizzie Simmonds, who set a British record in the 100m backstroke on the opening night, took gold in the 200m in a season's best 2:00.91, just outside her own British record.
Proud, 21, of the Plymouth Leander team, broke Mark Foster's 14-year-old short-course 50m freestyle British record on the opening day, clocked 46.69 in the 100m freestyle and on Sunday added the 50m butterfly with a time of 22.39 seconds.
Willmott, 22 - who also won gold in the 200m IM and 400m freestyle, plus silver in the 200m butterfly - captured the 400m title in 4:28.26, an impressive six seconds ahead of the rest of the field.
Stockport Metro's Liam Selby took gold in the men's 50m butterfly with a narrow victory in a time of 23.56.
Anna Hopkin of Bath University lowered the personal best time she posted in the morning heats to win 50m freestyle gold in 24.44.
A superb anchor leg from Rebecca Turner guided the City of Sheffield, also featuring Maya Westlake, Darcy Deakin and Ellie Faulkner, to gold in the women's 4x100 freestyle relay in 7:53.70.
Calum Tait finished more than a body length ahead of the next placed swimmer in the men's 200m breaststroke, posting a personal best 2:05.42.
The women's 200m freestyle final went down to the final touch but it was Loughborough University's Sophie Smith who touched first to take gold in 1:56.03, only 0.02 seconds outside her lifetime best.
In the men's 200m freestyle final, Loughborough University's Adam Barrett won in a season's best 1:43.72.
Ben Proud claimed his fourth British record of the ASA National Winter Meet on the final day in Sheffield.