Parcel deliveries, where competition from the likes of FedEx and UPS have eaten into Royal Mail's market share, rose 3 per cent.
Under Ms Greene, the company has embarked on an ambitious cost-cutting drive and the company confirmed that it reduced its headcount by 3,500 over the year.
Ms Greene added: “We are introducing new and improved products and services and responding quickly to changing customer needs.
“These measures, alongside our emphasis on customer focus and delivering a value for money service, have helped us to maintain our pre-eminent position in UK letters and parcels and driven growth.”
In the UK, revenue fell 1 per cent to £7.6 billion as letter volumes fell by 3 per cent.
Adjusted annual operating profits before transformation costs - Royal Mail's preferred measure of performance - rose 5 per cent to £742 million.
The 500-year-old company was privatised in 2013 and listed on the London Stock Exchange.
Shares were down over 3 per cent at 491p in morning trading.
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Dave Ward, Communication Workers Union general secretary, said: “Royal Mail Group's strong financial performance, in the face of tough market and regulatory pressures, show the company is well placed to deliver future growth and innovation in the business, working closely with the CWU.
“The continued fall in letter volumes and the significant level of competition Royal Mail already faces should serve as a reminder to Ofcom that protecting daily deliveries should be the number one priority of its review.”
PA
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