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Aung San Suu Kyi was invited to visit Britain when she met Prime Minister David Cameron in Yangon on Friday.
At the time, she said the fact that she would consider the offer, rather than reject it outright, showed "great progress" had been achieved in Burma.
Suu Kyi, 66, was first detained in 1989, and spent 15 of the next 21 years in detention, refused to leave the country during the brief periods when she was not held by authorities, for fear of not being allowed to return.
Her long refusal to leave Burma characterised her steely determination to defy the ruling junta, which offered to release her from house arrest to be with her late husband, Michael Aris, who died of cancer in Britain in 1999.
Nobel Peace Prize laureate and newly elected lawmaker Aung San Suu Kyi will travel outside Burma for the first time in 24 years after accepting invitations to visit Norway and Britain in June, her party have told the Reuters news agency.
Her travel caps months of dramatic change in Burma, including a historic by-election on April 1st that won her a seat in a year-old parliament that replaced nearly five decades of oppressive military rule.
Her trip will include a visit to British city Oxford, where she attended university in the 1970s, said National League for Democracy (NLD) party spokesman Nyan Win.