And in another body blow to Jeremy Corbyn, a different poll found less than half of Labour voters think he is the best person to lead the country.
A ComRes poll for the Independent and Sunday Mirror put the Conservatives four points up at 46 per cent while Labour remains unchanged on 25 per cent, the Lib Dems on 11 per cent and Ukip on 9 per cent.
A separate survey for the Observer found just 45 per cent of Labour supporters back the leader as the best prime minister for the country in a head-to-head choice between him and Theresa May.
Jeremy Corbyn's popularity has slumped while Theresa May continues to dominate the polls
Theresa May's Tories have opened up a 21-point lead over Labour
Among all voters, support for Mr Corbyn entering Downing Street slumps to 14 per cent with Mrs May given the nod by 47 per cent in a two-way contest, according to the Opinium poll.
The findings come as Mr Corbyn faces yet more attacks on his leadership ahead of next month's local elections after Labour lost a Middlesbrough council seat to the Tories in recent days on a by-election swing of eight per cent.
Labour MP for Middlesbrough South and East Cleveland Tom Blenkinsop, a strong critic of Mr Corbyn, said: "We lost due to the leader's name being mentioned on the doorstep as the reason why residents were not voting Labour."
Jeremy Corbyn is still struggling to gain support
We lost due to the leader's name being mentioned on the doorstep
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When asked which party was most trusted to lead Brexit negotiations, 35 per cent backed the Conservatives, the same as last month, while Labour's rating stayed static on 12 per cent, the Opinium poll said.
Health and Brexit remained the most important issues among voters, but terrorism climbed from fifth to third place in the aftermath of the attack at Westminster.
Labour, on 28 per cent, enjoys an eight-point lead over the Tories when it comes to the NHS, but Mr Corbyn's party was named by just seven per cent as having the best policies on immigration – the fourth most important issue to those questioned.
Theresa May's political career in pictures Thu, April 6, 2017
Prime Minister Theresa May has promised to 'build a greater Britain'
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Saudi Arabia's King Salman bin Abdulaziz al-Saud (R) meeting with British Prime Minister Theresa May in the capital Riyadh, Saudi Arabia, 05 April 2017. May is visiting Saudi Arabia as part of her Middle East trip to boost diplomatic ties in the region
The ComRes poll found US President Donald Trump's missile strikes on Syria were backed by 38 per cent and opposed by 35 per cent in the UK.
Asked whether Foreign Secretary Boris Johnson was a hindrance to the Government's foreign policy objectives, 37 per cent said yes and 32 per cent said no.