As her country struggles to emerge from decades of military oppression, Aung San Suu Kyi received a vivid insight yesterday into what makes headlines in a stable democracy.

In a surreal moment at a Downing Street press conference with David Cameron, a journalist suddenly bracketed a question about Burma's future with a challenge to the Prime Minister over the tax arrangements of Take That's Gary Barlow. With a faint smile, Ms Suu Kyi told her host: "I think I have got the easier question."

Her visit to No 10 – followed by a historic address to MPs and peers – was tinged with poignancy for the Nobel peace laureate. In her speech she recalled a photograph taken of her father, wrapped in a British military greatcoat, in Downing Street in 1947 – months before his assassination, and the year before her homeland gained independence from Britain.

Ms Suu Kyi became the first woman apart from the Queen, and the first non-head of state, to be invited to speak in Westminster Hall.

Most of the Cabinet and hundreds of MPs, peers and parliamentary officials packed into the medieval building to hear her speak of the inspiration she has drawn from Britain's centuries-old democracy. She even praised the weekly punch-up between David Cameron and Ed Miliband, saying: "It is when Burma has its own satisfactory equivalent of Prime Minister's Questions that we will be able to say that parliamentary democracy has truly come of age."

She also made clear she was not starry-eyed about the fustier side of Westminster, poking gentle fun at the time spent debating whether she was an appropriate person to be invited to speak.

Describing the response she had received in Britain as very moving, she said the BBC had kept her in touch with the outside world during her years of house arrest and added that listening to music and reading biographies persuaded her she would never be alone.

But Ms Suu Kyi, who completes her four-day visit to Britain today, stressed: "This journey out of Burma has not been a sentimental pilgrimage to the past, but an exploration of new opportunities for the people of Burma."

She used her platform to appeal for help developing a stable parliamentary democracy in Burma, rebuilding its education system and encouraging companies to invest in the country.

"Our own determination can get us so far. The support of the people of Britain and of peoples around the world can get us so much further," she said.