Nobel peace laureate Aung San Suu Kyi has been given David Cameron's backing for efforts to amend the Burmese constitution which prevents her standing for president in 2015.
The Prime Minister, who said he was one of Ms Suu Kyi's "greatest admirers", pledged to build international pressure for the constitutional changes.
Welcoming her to Downing Street, Mr Cameron said Britain would do "everything we can" to support Ms Suu Kyi in her efforts to change the constitution, which will require the agreement of the current president Thein Sein and the military.
Mr Cameron said: " You are hugely admired in this country, I am one of your greatest admirers - for everything that you have done for your country but also for everything you stand for in the world.
"Your example and your perseverance in your beliefs is a huge inspiration to people across Britain and people around the world. We wish you well with everything that you are doing and want to do everything we can to support you."
He said there had been progress on human rights in the country, with the release of political prisoners and Ms Suu Kyi's National League for Democracy winning seats in a by-election.
But he added: "The most important message is that progress needs to be sustained and, in particular, we need to see the constitution amended.
"It would be completely wrong for elections to be held under a constitution that really excludes one person, who happens to be the leader of democracy in Burma, to be excluded from the highest office in the land.
"Those would be no elections at all, in my view. Those would not be democratic elections, the constitution has to be changed in that way and in other ways.
"We will do everything we can to build the international pressure to send the clearest possible message to the Burmese government that these changes must be made."
Ms Suu Kyi said: "The crucial issue at the moment is to make amendments to the constitution. If the process of democratisation is to move forward, if it is to be sustainable, we have to amend the constitution to make it a democratic one, one that will ensure that the future of our society is going to be rooted in genuine democratic institutions."
On her second visit to the UK after her release from house arrest, she said she wanted progress to be "i nclusive of all those in our country who want to be a part of the process of development and democratisation".
The Burmese opposition leader added: "Although there has been some progress there has not yet been enough and in order to carry it forward we have to address this very important issue of constitutional change, of inclusive development which must have, at its heart, providing jobs for our young people and for others."
Asked about progress on religious freedom and citizenship, Ms Suu Kyi said: "It's for the president and his government to set a timeframe for their policies with regard to citizenship or any other matter that the government has to deal with.
"If you want me to give you a timeframe you had better make sure that I become president."
The Prime Minister added: "I think that's a brilliant point on which to end, we look forward very much to welcoming you back to No 10 Downing Street after that great day."
International Development Secretary Justine Greening said: " Rangoon General Hospital has offered life-saving healthcare to the Burmese people for generations and it is right that we help Aung San Suu Kyi in her work to restore this crucial institution.
"Her project shows that Burma is getting back to business and I am pleased to support this and the country's wider agenda of healthcare reform."
Ms Suu Kyi also met Labour leader Ed Miliband, who said she was an "inspiration to politicians across the world".