Williams have insisted that Jenson Button will drive for them in 2005 despite BAR's attempt to keep him.
Williams gave Button his F1 break in 2000
Team owner Frank Williams said: "We are of the firm opinion on strong legal advice that BAR have lost the opportunity to retain Jenson.
"I have no doubt he will be with the BMW Williams F1 team for 2005."
Williams said he only went public after he learned that BAR were to break the story to a British newspaper and wanted to resolve the dispute "amicably".
But he admitted that it might go to F1's contract recognition board, or even to the British courts.
He added: "Whatever is said about contractual details, one fact is not contestable. Jenson wishes and expects to drive for the BMW Williams F1 team in 2005 and 2006 and has made this intention clear."
Williams gave Button his break into F1 in 2000 and said that his team had held "a form of option [on Button] since the end of '00", when the team released him in favour of Juan Pablo Montoya.
That option, he said, was "subsidiary to the BAR option, but had precedence".
But he said he had had "no anticipation" that Button would be on the market for 2005 until Button's manager John Byfield approached Williams late last month.
Williams said Byfield sent BAR boss David Richards a letter saying the option was "invalid, not exercised properly and that he had already entered into a conflicting contract with Williams for Jenson".
"I called David Richards approximately five minutes after I knew he had received that letter and said we wanted to handle it privately, and that if there was disagreement then the first step would be the contracts recognition board. I had no intention of going public."
Williams only released news of his deal with Button after he learned late on Thursday that Richards had spoken to the Times, he said.
Williams added that he was optimistic his team could put this year's disappointing form behind them.
"You might ask why an intelligent and thoughtful driver like Jenson has asked to join Williams against the current run of form in the championship," Williams said.
"As I see it there are two reasons for this.
Button and Webber are set to be team-mates
"Firstly, we have enjoyed a long, open and honest relationship with Jenson since he started with us in F1 and we have maintained contractual links ever since.
"Secondly, he has seen the significant investment and reorganisation we have undertaken and he believes his best path to a world championship is with this team.
"Whether our team with Mark [Webber] and Jenson together will be strong enough to beat Ferrari is an unanswerable question because the other part of the equation is our motor car.
"Clearly, we have been deeply embarrassed by our poor performance this year and there is a lot of anger and hard work at present in this company to rectify that situation properly for this year."
Williams technical director Sam Michael said Williams had made errors in two or three different areas of the car, that could be rectified for next year and he was confident Williams could "put it right" for 2005.