July 5 (Reuters) - British budget airline easyJet said on Sunday it had accepted an improved takeover offer from U.S. private equity firm Castle Lake, valuing the British company at up to 5.5 billion pounds ($7.34 billion), in a move that could potentially be a game-changer for the European aviation sector.

The new offer of £6.90 per share represents a 73 percent premium over EasyJet's closing share price on May 29, when Castle Lake first revealed its interest in the airline to British regulators, leading to a sharp rise in the share price since then.

EasyJet operates low-cost flights to 38 European destinations and faces operational challenges amid the Iranian conflict, which has led to a sharp rise in jet fuel prices, reducing profit margins for airlines worldwide.

EasyJet rejected a £4.93 billion bid from Castle Lake in June but expressed interest in continuing talks by granting the US firm limited access to the company's commercial data.

Analysts had raised questions about whether Castle Lake was able to comply with EU regulations requiring that airlines operating in the EU be majority-owned and managed by European citizens.