* Lib Dems promise to block further tax cuts for wealthy
* Junior coalition partner struggling in opinion polls
* Parody of Clegg apology goes viral on Internet
* Party members anxious but back Clegg for now
By Tim Castle and Matt Falloon
BRIGHTON, England, Sept 26 (Reuters) - Britain may have to increase taxes on the rich to reduce its record budget deficit, Liberal Democrat leader Nick Clegg said on Wednesday, hoping to rally his centrist party behind him after a public apology that many found embarrassing.
The deputy prime minister has seen voters desert the Lib Dems since he agreed to form a coalition government with the Conservatives in May 2010. Polls indicate he faces disaster in the 2015 election unless supporters return.
Now ranked Britain's least popular political leader, Clegg has been mocked since releasing a video ahead of his party's annual conference apologising for breaking a campaign pledge not to raise university student fees, only to triple them once in power.
Swiftly re-edited by internet satirists who made Clegg sing "I'm sorry, I'm sorry" over and over again, the video has received more than 1.5 million clicks on YouTube, adding to his humiliation.
In his main speech of the conference, Clegg defended his decision to back the unpopular austerity cuts proposed by Prime Minister David Cameron's centre-right Conservatives, and pitched his party as a restraining force in the coalition.
"If we have to ask people to take less out or pay more in, we'll start with the richest and work our way down," he told party members in the southern resort of Brighton.
He ruled out further cuts to the top level of income tax following a 5 pence reduction to 45 pence in the pound announced in an unpopular budget in March.
"All future cuts in personal taxation must pass one clear test: Do they help people on low and middle incomes get by and get on? It's as simple as that," he said.
But the conference - traditionally an arena to reassure supporters and gain domestic media coverage of key messages for voters - was overshadowed by his apology over tuition fees.
Coffee mugs decorated with Clegg's face and the words "I'm sorry" sold out swiftly from an exhibitor's stall in the seafront convention centre.
Clegg was once hailed as the herald of a new era of honesty in politics, but his failure to deliver a cornerstone policy promise in the Lib Dems' first experience of government has badly damaged their re-election prospects.
"Nick Clegg is one of the worst leaders the party has ever had, and is just politically inept, and is appallingly badly advised," party activist Roger Hayes, 59, said on the conference sidelines.
At a question-and-answer session, Clegg made a personal appeal for forgiveness to one member who challenged him on the party's fall from grace.
"No one has struggled with this more than I have," Clegg said. "No one has tried to be as upfront as publicly as I have in this last week about the fact that we were wrong. We made a mistake, for which I have apologised."
Clegg, 45, briefly ranked as the most British popular politician since wartime leader Winston Churchill after outshining his Conservative and Labour rivals in a pre-election television debate.
But the broken promise on tuition fees, which led to riots around parliament, and public anger over austerity measures have devastated his public reputation as a politician to trust.
The fate of Clegg, his party and its Conservative partners may ultimately depend on an economy expected by most economists to contract this year despite government forecasts of growth.
But an ICM poll for the Guardian newspaper suggested the Lib Dems' popularity would rise by five points if Vince Cable, the left-leaning business secretary, took over as leader.
Current surveys suggest the party would lose up to half its 57 members of parliament if an election were held now, and that it will also lose more ground in local authorities, its grassroots power base, where it has already lost a third of its seats in two years.
While members at the conference grumbled, there was little enthusiasm for ditching Clegg before the 2015 election.
"The vilification has been quite ridiculous," said Jean Evans, 67, a former councillor from Chester, northwest England.
"The more people have been calling Nick ridiculous names, the more I have come to respect him, because he hasn't given up, he hasn't crumbled, and he has just got on day after day with his job. And I think that is tremendous."