Last Wednesday, on my third day as the shadow work and pensions secretary, the latest unemployment figures were released.
Mr. Blunkett returned to the government as work and pensions secretary.
Yvette Cooper, the shadow work and pensions secretary, has also ruled herself out of contention.
Liam Byrne, the shadow work and pensions secretary, said the letter suggested ministers had not come clean over the effects of their policy.
Labour must oversee a "radical" rethink of the welfare state for the 21st century, the shadow work and pensions secretary said.
The former work and pensions secretary resigned from the cabinet last June, urging Gordon Brown to stand down.
We have stuck closely to the recommendations of the former Labour Work and Pensions Secretary throughout this process.
Walker added that the review by Lord Hutton, the former Labour work and pensions secretary, should be upheld.
An independent commission led by Lord Hutton, the former Labour work and pensions secretary, has outlined proposals for the government to consider.
The shadow work and pensions secretary, Liam Byrne, was working hard on tough decisions with announcements soon on welfare.