The Conservatives have surged to sit alongside Labour in the polls for the first time in nearly 18 months, largely owing to a sharp fall in support for Ukip, according to the latest ICM monthly poll for the Guardian.

Labour will be alarmed that the two main parties are neck and neck despite the economy showing only tentative signs of starting to recover.

ICM's telephone poll last month showed a strong Labour lead of seven points, but this month the Tories are benefiting from the continuing collapse in support for Ukip, down from 18% in May – just after its local election success – to 12% in June and now just 7%.

The shares of the vote are Conservatives 36% (+7 on last month), Labour 36% (no change), Liberal Democrats 13% (+1), Ukip 7% (-5), and others 8% (-2).

It is the best result for the Tories in an ICM poll since they led by three points in March 2012, just before George Osborne's mishandled budget presaged a series of other errors across the government machine.

The fall in the Ukip share may reflect the recent comparative decline in publicity for the party's leader, Nigel Farage, and Downing Street's persistent efforts to neutralise Ukip's appeal by countering with a series of strong messages on immigration, welfare and a referendum on UK membership of the European Union.

It may also suggest that Ukip support is in part a protest vote exercised in relatively unimportant local elections and that this support dissipates once the protest has been registered.

Ukip is likely to argue that the drop in support has not been reflected in most other polls. At the weekend four online polls showed Ukip support in the high teens, but a new Populus poll showed Ukip on 10%.

Farage's party will also be banking on a big resurgence of interest during the European parliament elections next June, when it will hope to come first in terms of national share of the vote.

The ICM poll findings do not appear to reflect any change in the underlying support for Labour since the party's standing of 36% remains unchanged on last month – although party supporters may hope to dismiss it as an outlier.

By contrast, the running YouGov daily online poll shows Labour leading by about 11 points, a hardening in its ratings after an apparent softening in the previous fortnight.

The ICM poll also contains a clear warning for the chancellor: two-thirds (65%) do not believe his promise, made last week, that the deficit can be cut after the election without raising taxes.

There is a majority scepticism on this issue across the political spectrum, with 57% of people who voted Conservative in 2010 agreeing (2010 Lab, 70%; 2010 Lib Dem, 75%).

That suggests the Tories will struggle to damage Ed Miliband and Ed Balls in the next election campaign simply by warning of a Labour tax bombshell if elected.

The findings may also reflect the unwillingness of any voter to answer positively if asked a question that implies the respondent trusts a politician.

At the weekend the Lib Dem business secretary, Vince Cable, threw a new argument into the likely election tax and spending debate by saying he did not believe the last Labour government had spent too much in the run-up to the banking crash, but instead had failed to regulate banking.

Other Lib Dems, including the deputy prime minister, Nick Clegg, have persistently argued that the deficit was created by Labour overspending before 2008.

But overall, the Conservatives will be delighted with the ICM findings. Conservatives are convinced that as growth picks up over the next 12 months, the polls will swing decisively to them.

Cameron is also due to take the cabinet to a celebratory "away day" at Chequers on Thursday, where they are expected to hear political as well as government briefings before parliament goes into recess. A reshuffle in the ministerial ranks outside cabinet, which had been pencilled in for this week, now looks likely to take place in the autumn.

Conservative ministers are privately sceptical that they have drawn level with Labour yet, basing their judgment on other polls and doorstep response. They still maintain it will be very hard to win an overall Commons majority.

Ed Miliband's brother, David, in a valedictory TV interview at the weekend, cautioned against the conventional wisdom that a hung parliament was likely after the next election. The British public may move decisively in favour of one of the main parties, he said, adding that there was still a "great danger" they might choose the Tories.

Lib Dems will be concerned at the absence of any sign in the ICM poll that their overall vote is picking up, despite the decline in Ukip support.

The findings appear to confirm the Lib Dems are no longer seen as a protest party, making it harder to win a new constituency.

Danny Alexander, the Lib Dem Treasury chief secretary, will on Tuesday publish the result of a Cabinet Office-led review into a replacement for the Trident nuclear deterrent. The ICM poll shows the public split on the issue.

Three in 10 (31%) think Trident should be replaced (rising to 45% of those who voted Tory in 2010), while an identical number (31%) think it should be slimmed down (rising to 37% among 2010 Lib Dem voters) and 30% think we should no longer have any deterrent (39% among Labour 2010 voters).

In his speech, Alexander is to back a limited replacement.

The poll also shows all three party leaders have judged the public mood correctly by rejecting the 10% increase in MPs' pay from 2015 proposed by the parliamentary watchdog. The proposed rise would take MPs' pay to £74,000 in 2015.

The public believe MPs should be paid a shade over £50,000 (£51,620 on average). Men are happier to pay more – at £54,000 – while women think MPs should be paid £49,000. A clear correlation between social grade and pay was revealed: those in the most affluent group, AB, suggest MPs should get £58,000, C1s suggest £55,000, C2s £46,000 and DEs £45,000. Lib Dem voters are the most generous (£61,000), as are people living in the south (£54,000).

• ICM Research interviewed a random sample of 1,003 adults aged 18+ by telephone on 12-14 July 2013. Interviews were conducted across the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.