His six-month-old son, Zachary, was born 10 weeks premature at the hospital last December and weighed just 2lb 3oz.
Mr Walton's attempt started on Thursday and finished at 2000 BST on Saturday. Now he awaits the verdict of Guinness World Records scrutineers.
"Apart from the fact that my back is killing me, it went really well," said the 32-year-old.
£1 per item
Mr Walton was allowed a five-minute break every hour and could accumulate them into a maximum 30-minute break.
The record stood at 55 hours and 5 minutes.
People donated £1 per item to have their clothes ironed.
Mr Walton, who owns the dry cleaning outlet at the Asda store when he attempted the record, had two official adjudicators with him at all times and had to iron the clothing to a good standard.
He added: "This is the first part of my attempt to raise £25,000 towards buying an incubator.
