The scandal over his tax dealings and a steel sector crisis have badly bruised Prime Minister David Cameron just three months ahead of a crucial referendum on Britain's EU membership, experts said.

Cameron and his Downing Street office issued four comments regarding the Panama Papers before the British leader on Thursday finally admitted he had held shares in his late father's Bahamas-based offshore investment fund.

Cameron's popularity has slipped in recent weeks, with only 34 percent of respondents saying they thought he was doing well and 58 percent that he was doing badly, according to a YouGov poll released on Friday.

His previous popularity rating in a similar poll in February was 39 percent and 53 percent.

Labour opposition leader Jeremy Corbyn instead has seen his popularity rise from 25 to 30 percent, while those who think he is doing badly fell from 59 to 52 percent.

Labour has accused Cameron of "hypocrisy", pointing to his crusading stance on tax evasion and avoidance and his promise of enacting change at an anti-corruption conference in London next month.

"The prime minister has lost the trust of the British people," Corbyn said.

Scottish First Minister Nicola Sturgeon joined the criticism, saying the scandal "leaves his credibility in tatters and completely betrays public trust".

Ian Bond from the Centre for European Reform think tank said: "His ability to lecture the others at the anti-corruption summit is going to be damaged."

But he added: "Most of these political scandals pass quickly."

"It's not great news for him but we are weeks away from the referendum so he still has the chance to get back," he said.

- 'Sixth sense' gone? -

Ramon Pacheco Pardo, a lecturer at King's College London, said: "When his government for example is asking companies to pay their fair share of tax, when he's asking individuals to pay their taxes in full, obviously his political capital is really diminished."

There has been criticism from within Cameron's own camp too.

"His politician's sixth sense seems to have deserted him," Paul Goodman, a former Conservative MP, wrote on the Conservative Home political blog.

"The prime minister doesn't always manage to keep his temper... and his original instinct may have been, when confronted with claims about a father that he loved, to tell the media to take a running jump.

"The EU referendum is sapping his and Downing Street's energy, focus and judgement -- just as it did over Port Talbot last week, the threat to the future of which clearly caught the government machine on the hop."

Cameron has been put under pressure by Tata Steel's announcement that it intended to sell some or all of its British operations including Port Talbot in Wales, putting 15,000 jobs at risk.

The government was accused of putting close trade relations with China, which has been exporting steel at cheap prices, over protecting steel jobs.

- 'Euroscepticism rising' -

There was more bad news this week when the Dutch voted against an EU-Ukraine trade deal -- a referendum seen as reflecting eurosceptic sentiment.

Brexit supporters cheered the result and said it was a good sign for their own campaign for Britons to vote to leave the European Union in a referendum on June 23, while Cameron played down the significance.

Bond said the Dutch vote would likely have "no direct impact on the Brexit vote" but was the result of "euroscepticism rising across Europe."

Cameron has staked his political future on the EU referendum and the latest polling shows the "Leave" and "Remain" camps neck and neck.

The British leader holds weekly public events to try to win over sceptical Britons but is on the defensive in the campaign too over a taxpayer-funded pro-EU leaflet to be sent to all British households.

Brexit campaigners cried foul over the government mailshot -- costing £9.3 million (11.5 million euros, $13.1 million) -- and an online petition calling for the government to stop campaigning with public money has gained more than 100,000 signatures.