Anti-Brexit campaigner Gina Miller has told the Lib Dems she is not their “leader in waiting” but “feels a bond” with the party on many issues.
The businesswoman, who won a Brexit court case against the government in 2017, is addressing activists amid talk over her future political ambitions.
She said she was not affiliated to any party but was a “friend” of the Lib Dems and backed their Brexit stance.
She urged Brexit opponents not to stay silent but to shape the debate.
Ms Miller has been linked to the Lib Dem leadership since Sir Vince Cable said last month he would stand down once Brexit was either resolved or stopped and said he wanted the contest to succeed him to be opened up to non-MPs.
Sir Vince has refused to set a date for his departure, saying he has a “series of tasks” to complete – including seeing through internal reforms designed to turn the party into a wider “movement for moderates”.
Ms Miller has ruled out an “official” career in politics but, on Friday, launched a personal campaign to “let the people decide for themselves” on Brexit.
The investment manager has been a prominent figure in the Brexit debate since successfully winning a legal challenge in 2017 which forced the government to get Parliamentary consent before giving notice of its intention to leave the EU under the Article 50 process.
The BBC’s Brian Wheeler in Brighton
She doesn’t want to lead their party, or even join it, but Lib Dem members seem to love Gina Miller anyway.
“I think it was amazing,” said Emmanuel de Kadt, a Lib Dem member from Brighton, “There was a bigger ovation for a non-member than anybody else so far.”
Riccardo Macuso, from Reading, hailed her “extreme bravery” in the face of “very aggressive” right-wing opposition.
“If we end up with somebody like Gina Miller (as leader) in the future it would not be such a bad thing,” he added.
Former MP Michael Meadowcroft said it was an “extremely well-judged” speech, just the kind of oratory that Lib Dems love. But, he added, “you cannot lead a party from outside Westminster”.
She told the conference in Brighton that she was not a member of the party and has no ambition of succeeding Sir Vince.
“I speak to you as a friend and someone who feels a bond with you on many issues… but I am not addressing you as leader-in-waiting” she said.
“I want to see the Lib Dems thrive because, in a health democracy, we need a strong third party, every bit as much as we need a strong opposition and, for that matter, a strong government and prime minister.”
She said the Lib Dems’ “reasonable, sensible, conciliatory” approach to Brexit needed to be heard, more than ever, with about six months to go until the UK leaves on 29 March 2019.
“We need statesmen and women doing what they genuinely believe is right for the country – not just reflecting society but shaping it.
“None of us is going to be forgiven by these future generation if we tell them we decided just to sit this particular national crisis out, just waited to see what would happen, felt there was nothing we could do or, worse, stayed silent and hoped others would sort out the chaos.”
On Friday, Ms Miller – who it is understood will not be speaking at either the Labour or Conservative conferences – launched a personal campaign providing “unspun facts” about the choices facing the UK and the different plans put forward by MPs.
Although she has not specifically come out in support of the People’s Vote campaign for another referendum on the outcome of the Brexit negotiations, she said it was “time for politicians to do the morally and democratically right thing to let the people decide their own future on the facts before it is too late”.
The People’s Vote campaign has gained momentum in recent months, with leading unions and a growing number of Labour and Conservative MPs backing it.
But Theresa May has repeatedly ruled out another vote, insisting the UK has a choice between her Chequers plan and leaving without a deal. Labour’s Jeremy Corbyn has said another referendum is not party policy, with a general election the party’s favoured option.
Speaking in a Brexit debate on Monday, former Lib Dem leader Lord Campbell said a new referendum was “not a privilege for which we have to beg… it is a right” that people were entitled to.
Remaining in the EU would help the UK and Europe “stand up to the bullying” of US President Donald Trump and the aggression of Vladimir Putin’s Russia, he added.