Updates with details of the deal, background

July 5 (Reuters) - British budget carrier easyJet EZJ.L said on Sunday it has reached an agreement in principle with Castlelake on a sweetened £6.90-per-share takeover proposal from the U.S.-based investment firm.

The new offer values easyJet at £5.23 billion ($6.94 billion).

Castlelake had previously proposed £6.50 per easyJet share, which was rejected by easyJet.

Last month, in a bid to keep takeover talks alive, the airline had said it would grant Castlelake limited access to commercial data after the U.S. investment firm returned with an improved offer, signalling a willingness to engage further even as the airline rejected the latest £4.93 billion proposal.

($1 = 0.7490 pounds)