He will take on the post part time at the parent company of the Post Office until a permanent chairman is named later in the year.
Leighton will take on the role at a difficult time for the company, as it hopes to avert massive strikes over plans for swingeing job cuts at the company.
As well as holding a non-executive role at Lastminute, Leighton is chairman of BHS and a non-executive director of Dyson. He was appointed as a non-executive director of Consignia last April.
The previous chairman, Neville Bains, left the company late last year after the government was reported to be unhappy with his performance. Consignia saw its losses increase fivefold to £281m in the six months to September 2001.
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