Like-for-like sales at the chain rose 5% in the year to Saturday amid a recovering high street, while 16 new store openings across Europe and a strengthening euro also helped drive Primark's sales hike.
Lower discounts during its summer sale also bolstered the chain's profit margins for the year, its owner Associated British Foods (ABF) said.
Primark plans an "extensive" programme of openings in time for Christmas, and intends to add more than a million square feet of selling space during its new financial year, on top of about 800,000 sq ft opened this year.
Primark's latest store opens this week in West Bromwich to give it 257 branches, while its first store in France will open in Marseille in December.
A warm autumn last year ensured a strong start to the financial year for Primark, although freezing temperatures during March and April subdued growth. But summer trading was strong, driving the profits and sales boost, ABF said.
Analysts at Panmure Gordon hiked their underlying profit expectations for Primark to £505 million from £473 million, adding they expect "another strong year in 2014".
Meanwhile ABF said its Kingsmill bread brand has leapfrogged Hovis to claim number two spot in the UK market, behind Warburtons.
Its Allied Bakeries business benefited from growing volumes and a contract to supply the Co-op from April, which hiked Kingsmill's market share. But ABF added the market remains intensely competitive with some pressure on margins.
Silver Spoon sugar's sales and profits will be lower than last year reflecting an "especially competitive" year, it said. Its Jordans and Ryvita brands had an excellent year, helped by advertising campaigns, while its Twinings tea brand grew sales in all its major markets.
But ABF warned negotiations with European customers on sugar prices in 2013/14 were proving challenging, with "increasingly negative sentiment", driven by a glut of sugar and low global prices.
Europe plans to end sugar quotas for domestic production in 2017, which ABF said will mean continued downward pressure on European prices beyond then. However, it insisted it is well-placed to succeed as one of the world's lowest-cost producers.
Its sugar production of 1.14 million tonnes in the year to mid-September was lower than last year's 1.32 million due to a poor harvest. It also expects crop yields to be slightly lower than average in its new financial year. ABF said sales and profits in its sugar arm were in line with expectations during the year.
Analysts at Numis Securities lifted their 2013 pre-tax profits forecast for the group to £1.1 billion from £1.08 million.
But its shares fell 2.5% and Investec Securities analysts warned there may be "trouble beyond".
They said: "The big picture for us is that, with the sugars profit bubble deflating, it is now Primark that needs to carry the profit can for ABF going forward."