Gordon Brown was questioned about his future as premier during a visit to St Thomas' Hospital on Friday morning.
The Prime Minister, who was on his way to Lambeth Palace for talks with the Dalai Lama, was welcomed by hospital trust chair Patricia Moberly.
Following the overnight news of the Conservative win in the Crewe by-election, the Prime Minister was asked by a reporter if he thought that he retained the confidence of Labour Members of Parliament.
"The people want us to address what are very real challenges" replied Mr Brown who said that he acknowledged that people were concerned about fuel prices and the cost of food at the supermarket.
"The task that I have set for myself is that we take this economy through difficult times into a future where we have both fairness for all and prosperity for the British people," he said. "That is the challenge I am going to meet for the British people."
Accompanied by Health Minister and former nurse Ann Keen, the premier met Chief Nurse Eileen Sills and Matron of the Year Karen Bonner who took him on to the wards to meet the new matrons responsible for hygiene and infection control.