However, speculation persisted last night that some large shareholders remained unhappy with the terms of the original Lucas/Varity merger and would demand a sweetener in the form of a special dividend.
In a statement, BBA said it had "not been able to satisfy itself that Lucas shareholders would accept an alternative to a merger of Lucas and Varity Corp [of the US] on terms which would be in the interests of BBA's shareholders". BBA added that it would only make an offer with the agreement of the Lucas board.
BBA's climbdown came after three institutional shareholders - Fleming Investment Management, Standard Life, and Threadneedle Fund Management - had voiced concerns about a possible bid after meetings with Roberto Quarta, the BBA chief executive.
"We're not happy with it. We don't see the underlying industrial logic," said Peter Seabrook of Flemings.
Shares in Lucas fell 15p to 239p as bid hopes faded, but BBA remained unchanged at 303p, mainly on relief that an earnings dilutive offer for Lucas now seemed unlikely.
Earlier this week BBA said it was considering making a bid for Lucas, which at pounds 2.1bn is nearly twice the size of BBA.
BBA had been thought by industry sources to be considering a combined cash and share offer. Analysts also speculated that BBA would have had to sell the aerospace and diesel divisions of Lucas for around pounds 600m to make the deal more affordable.
Lucas said it felt the withdrawal of a threatened hostile bid by BBA endorsed the logic behind its planned merger with US automotive supplier Varity Corp.
"We're very happy with our excellent merger agreement with Varity, and I believe that the statement by BBA confirms that there is excellent shareholder value for our shareholders in the merger transaction, " said a Lucas spokesman. He added that there was "absolutely no question whatsoever" of the Lucas board initiating any dialogue with BBA.
Despite the BBA announcement, it is by no means certain that the Lucas/Varity merger is now a done deal. Other companies, such as German engineering groups Mannesmann and Linde, may yet enter the fray.
The Lucas/Varity merger is not expected to be completed by September, leaving a small window of opportunity for another potential predator.