Mr Blair thanked Mr Mitchell for the “support” he “always” receives from officials on his visits to Africa. In a handwritten section he added: “We are really excited by our capacity building work. I think it is a major part of a successful future for Africa.”

The letters were obtained by The Sunday Telegraph under the Freedom of Information Act.

AGI, which employs 29 people, was set up by Mr Blair in 2008. Run by Kate Gross, a former Downing Street aide, it has staff in Rwanda, Sierra Leone, Liberia and Guinea.

Its aim is to help the four governments to run more effectively and it intends to expand into other African nations.

Mr Blair’s office is adamant that his commercial activities are not in conflict with his charitable work and that he does no business in countries where AGI operates.

The precise details of the applications made by Mr Blair’s charities were not disclosed.

AGI applied last year to become part of DfiD’s tendering process to carry out “public sector governance” work — helping to improve governments in 28 countries across Asia and Africa.

Last year DfiD spent £787 million on “government and civil society” schemes and its budget will rise in total to £11 billion by 2015, having escaped the Government’s austerity drive.

In a separate bid — which was also unsuccessful — the charity sought a grant from the Government’s Global Poverty Action Fund, which distributes £40 million a year to organisations proposing to help reduce poverty in dozens of countries, including the four states where AGI is active.

The correspondence obtained from Dfid shows that as a result of separate discussions, Elizabeth Carriere, the head of DfiD’s Rwanda and Burundi office, agreed to attend meetings with AGI’s backers, including Lord Sainsbury, a prominent Labour donor who was a minister under Mr Blair.

A DfiD spokesperson said: “In 2011, the African Governance Initiative applied to DfiD for a Global Poverty Action Fund grant and to become eligible to compete for contracts on public sector governance.

"Both applications were conducted on an open and competitive basis. Neither application was successful.”

A spokesman for AGI said it was “completely normal” that Mr Blair should write to and meet both the Secretary of State and DfiD officials to brief them on the charity’s work.

“As patron of AGI, Tony Blair provides his time on a pro bono basis. Tony Blair has not raised the AGI proposals for partnership to which you refer with the Secretary of State or any other government official,” he said.

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Tony Blair's charity refused aid funding