Miliband said he was "gravely concerned" about the conflict there, while insisting that the government was listening to protesters a hunger striker continued his campaign in London.
"I remain gravely concerned at the continuing conflict in northern Sri Lanka that threatens many thousands of civilian lives," Miliband said in a statement.
"The British government maintains its calls for an immediate ceasefire in Sri Lanka and for civilians to be allowed to leave the conflict area."
Vijay Nambiar, Ban's chief of staff, has been sent to Sri Lanka to try to ease the plight of tens of thousands of civilians trapped by fighting between government forces and cornered Tamil Tiger rebels.
Britain -- a permanent member of the Security Council -- will ask Nambiar "to report immediately to the UN Security Council after his visit," Miliband said, adding that Prime Minister Gordon Brown's special envoy on Sri Lanka, former defence secretary Des Browne, was travelling to New York "to consult urgen