Protocol dictates that members of the Royal Family arrive last for a public engagement - with the Queen usually turning up just minutes before an event begins.
But Stewart and his wife, Penny Lancaster, blamed London traffic for their 10-minute delay while travelling from their Wapping apartment, and the singer apologised to the Prince when the pair eventually met.
Charles had already opened a Prince's Trust shop, near the City of London, called Tomorrow's Store, which sells jewellery, clothing, shoes and decorative objects designed by young entrepreneurs who have been helped by his charity.
After the apology, the two men were soon sharing a joke and when the Prince asked how the singer's voice was, Stewart replied "improving with age" and his wife quipped "like a lot of other things".
Stewart, a Prince's Trust Ambassador along with his wife, said afterwards that he always tells he children to be on time: "We have a place over in Wapping and it took us three-quarters of an hour to get here."
He added, laughing: "I wish I had my own police escort, I would always be on time."
Ms Lancaster praised the work of the Prince's Trust, which has helped young entrepreneurs through its business enterprise programme.
Referring to her husband, she said: "We both became ambassadors about 10 years ago. We are able to inspire and encourage our children, who have a strong support system and financial support. But what about the children that don't have that support system? The Prince's Trust is a real helping hand - it's fantastic."
The Tomorrow's Store is within the new offices of the Prince's Trust, which moved from its former home near London's West End to a building close to the financial heart of the capital after the lease on its previous premises expired.
Charles is taking part in a number of engagements this week to highlight the work of his charities, which Clarence House said had given business support to almost 400,000 and helped created more than 125,000 entrepreneurs.
During his visit to the new offices, Charles received two presents for his new grandson, Prince George of Cambridge.
Kimberly Smith, who runs a children's clothes shop in Port Talbot, South Wales, had some of her garments on sale in the new store and presented Charles with a baby bib decorated with the flags of the UK's four nations.
The Prince also accepted a blue romper suit decorated with elephants from Cecilia Crossley, chief executive of the company From Babies With Love, which donates its profits to good causes.
Ms Crossley's business has received marketing help from Arc, a programme run by the charity Business in the Community (BITC), which has Charles as its president.
The Prince met other business people who have benefited from Arc, which was established in 2011 and aims to connect social entrepreneurs in the Olympic host boroughs with expert support from companies like BP, Deloitte and Visa Europe.
Charles officially opened the new Prince's Trust offices and, speaking about the start of the Trust in 1976, told the staff: "I can never get over how everything has grown from such a small desk - one man and a dog - and I was the dog."
He added: "It is extraordinary for me just to see the expansion - in staff numbers, the huge numbers of people in different teams."
He went on to tell them he felt "pride" at the success people have achieved after being helped by his Trust.