Ofcom added: "For 1 April 2018 to 31 March 2019 the cap was set at 60p. Royal Mail increased its price for second-class stamps to 61p on 25 March 2019, thereby overcharging customers for seven days until the cap increased on 1 April 2019.
"The company estimated that it overcharged people by approximately £60,000 in total as a result, which it is unable to refund."
Gaucho Rasmussen, Ofcom's Director of Investigations and Enforcement, said: "Many people depend on postal services, and our rules are there to ensure they get a good service, at an affordable price.
"Royal Mail let its customers down, and these fines should serve as a reminder that we'll take action when companies fall short."
Royal Mail said: "We are disappointed with our first-class regulated quality of service performance in 2018-19. We accept and understand Ofcom’s decision."
On stamps the company added: "
On the stamps, it added: “We accept and note Ofcom’s decision around the 2019 second-class price cap. We made a mistake. Due to an error on our part, our price for second-class stamps was 1p above the requisite regulatory cap for seven days."