Labour's two-point fall in Opinium/Observer poll leaves it just one point ahead of the Tories, with Ukip up to 15%

Labour's support has slumped to its lowest level since soon after the 2010 election, according to a new Opinium/Observer poll. Ed Miliband's party now has a lead of just one percentage point over the Conservatives.

The findings – showing a clear bounce for the Tories after George Osborne's budget – will put more pressure on Miliband, whose party was 10 points ahead of the Tories a year ago.

The poll puts Labour on 33% (down two points on a fortnight ago), the Conservatives on 32% (up two), Ukip on 15% (down one) and the Liberal Democrats unchanged on 10%. Since the budget on 19 March, several polls have shown Labour's lead cut, but Labour strategists hoped the Tory bounce would be shortlived.

The Conservatives and Labour have not been so close in the polls since before Osborne's so-called "omnishambles" budget of March 2012 in which he abolished the 50p rate of tax and imposed other controversial taxes on pasties, caravans and charities.

The only comfort for Labour is that, as its support has fallen, the Conservatives have failed to record any strong increase and are still well down on previous highs in this parliament. In early March 2012 Opinium had the Tories on 38% and Labour on 36%.

Opinium poll Photograph: Observer

Labour officials insisted that the party would not change strategy or rush out announcements. Instead it intends to push harder on familiar issues such the cost of living, health, jobs for young people and fair ways to cut the budget deficit. Shadow cabinet members say several new policies will be unveiled in the summer when a policy review chaired by Jon Cruddas is completed.

While the Tories will be buoyed by the new poll, Ukip's score of 15% will alarm the Conservatives, and to a lesser extent Labour, ahead of a second head-to-head debate between Ukip leader Nigel Farage and Lib Dem leader Nick Clegg on Wednesday.

An instant poll found that Farage won the first debate, hosted by LBC Radio, with 57% of those questioned by YouGov for the Sun saying he performed best – against 36% for the deputy prime minister. The second will be televised by the BBC.

In an email to supporters, Clegg said the debate showed that the Lib Dems were the only party prepared to offer "a full-throated defence of our place in Europe", while the Tories and Labour were "riddled with division" on the EU.

Clegg said: "I am very proud that Liberal Democrats are prepared to stand up for Britain by issuing a full-throated defence of our place in Europe. It's clear we're the only party prepared to do so. The Labour and Conservative leaderships are bowing their heads and averting their gaze, desperate for the debate to move on.

"They may hold different positions on the EU, but their leaderships are treating it in the same way: a problem they don't want to talk about. "Both parties are riddled with division, more interested in themselves than standing up for our country."

• Opinium Research carried out an online survey of 1,936 GB adults aged 18+ from 25 to 28 March 2014. Results have been weighted to nationally representative criteria. Full tables and results are available online