* UK budget airline's founder had fought to oust chairman
* Rake has expanding role as Barclays deputy chairman
* EasyJet says search has begun for Rake's replacement
LONDON, Jan 26 (Reuters) - EasyJet Chairman Mike Rake will step down this summer, the budget airline said on Saturday, ending a fight by its founder and largest investor to oust him because of his expanding role as deputy chairman of Barclays.
Founder Stelios Haji-Ioannou urged Rake to leave last July after Barclays said he would spend more time with the British bank after the Libor interest-rate rigging scandal became public.
The airline rejected the call at the time and described it as being part of a "continuing campaign to undermine the good governance of the company."
Haji-Ioannou has had public disagreements with the airline's board over strategy, including whether it should expand and buy more planes. He founded the airline, with its distinctive orange branding, in 1995.
In a statement, Rake said he wanted to make his position clear before the company's annual general meeting on Feb. 21.
"EasyJet has by any definition enjoyed a period of success and profitable growth in the last three years," he said. "As this takes the airline to the threshold of entry to the FTSE 100 it is the right time for me to stand down."
Rake joined the easyJet board as deputy chairman in June 2009 and became chairman in January 2010. He is also chairman of BT Group.