Aug 10 (Reuters) - The takeover battle between tobacco giant Philip Morris (PM.N) and private equity firm Carlyle (CG.O) for inhaled treatments maker Vectura (VEC.L) will not be heading to the auction ring on Wednesday after Carlyle said it will not raise its bid. U.S.-based Carlyle on Tuesday declared final its 155 pence per Vectura share offer, which it sweetened last week to value the British company at about 958 million pounds ($1.33 billion). The proposal is below an increased 165 pence bid from Philip Morris on Sunday. Britain"s takeover regulator on Monday had intervened in the battle, saying that it would enter a rare head-to-head auction if the bidders do not make final bids by Tuesday 1600 GMT (1700 BST). read more Only a handful of British takeover fights have gone to auction, with the highest profile in recent years being the battle in 2018 for pay-television group Sky when Comcast (CMCSA.O) emerged as the winner of a single-day three round blind auction. read more London-listed shares of Vectura closed at 163.4 pence on Tuesday after hitting a more than five-year high of 176 pence earlier in the session. They have gained 33% in value since Carlyle"s first offer in May. Vectura has been the target of several approaches since May from the U.S.-based groups, which are eyeing the drugmaker"s expertise with inhalable formulations and device designs for respiratory therapies for illnesses such as asthma. read more The London-listed company had voiced its support for the Carlyle offer last week, saying that it may be better positioned under the ownership of the private equity firm, while noting the uncertainties that could arise for its stakeholders as a result of being owned by the Marlboro cigarette-maker. However, Vectura withdrew its backing and also withheld support for the higher offer from Philip Morris following the intervention from the Takeover Panel. Vectura did not immediately respond to a request for comment. A deal with either one of the U.S. companies would require shareholder approval. ($1 = 0.7229 pounds)