Queen Elizabeth II left Ireland on a triumphant note after finally getting a chance to mingle with cheering crowds, despite security concerns.

Adults and schoolchildren roared their delight as the Queen walked out of the English Market and chatted with onlookers who had waited patiently for a glimpse of her during her brief trip to Cork.

The atmosphere in Cork was more relaxed and jubilant than it had been in Dublin, where a bomb was discovered on a suburban bus hours before her arrival, ratcheting up fears of a dissident attack on the Queen, who was making the first visit by a British monarch to the Republic of Ireland.

She seems to have won rave reviews for her speech on Wednesday night, when she directly addressed the tense relations that had often left the two neighbours wary, despite cultural, family and business ties.

The Queen did not apologise for English actions, but expressed sympathy and regret for those who had suffered, striking a chord with many Irish listeners who said they were moved by her sincere and dignified approach.

Pat O'Connell, who showed the Queen and her husband, Prince Philip, his vast supply of fresh fish - including the wild salmon the Queen favours - said the monarch had accomplished her goals for the ambitious trip.

"We are absolutely thrilled, it has been the most wonderful trip," he said.

"The woman has just shown such dignity, such grace. You can say 99.99 per cent of the people are thrilled."

His views were echoed by other shopkeepers. Some said they were nationalists who wanted a united Ireland but had still been charmed by the Queen.

Radio talkshows were filled with praise for her, and TV commentators hailed her visit as a watershed event.

A palace spokesman, speaking on condition of anonymity because of palace policy, said the trip had surpassed expectations.

"It's been the most amazing four days," he said. "It's had a significance above and beyond a normal state visit. It's one of the most significant visits of her reign, without a doubt."

- AP