Voters approve of the Conservative-Liberal Democrat government so far, according to the first Guardian/ICM poll to be published since the general election.

There is also widespread support for changes to the electoral system, with people apparently sanguine about the prospect of further hung parliaments.

But today's poll suggests the Lib Dems have suffered some damage after deciding to join the Tories in government, with almost a fifth of those who backed the party this month saying they might be less likely to do so in the future. Support for the party has also dropped three percentage points since the general election, to 21% – although that remains higher than in many pre-election ICM polls.

There is no sign of a widespread movement of Lib Dem voters to Labour, with most people who voted Lib Dem this month saying the decision to join the coalition would make no difference to their decision to support the party. A quarter say it will actually make them more likely to vote Lib Dem.

In a theoretical immediate general election, both the Conservatives and Labour would gain ground. Tory support is now 39%, just over 2 points up on the election, while Labour support is 32%, also two points higher. Some of that support comes from the Lib Dems and some from other smaller parties, whose support is now two points lower than it was at the election.

There is also a notable gender gap: 25% of women say they would vote Lib Dem now, against only 16% of men.

Overall, 59% of voters say they approve of the decision to form a coalition and 32% oppose it. Tory voters are most enthusiastic, with 81% in favour and only 16% against. People who voted Lib Dem are slightly less keen about the deal that put the Conservative leader David Cameron in power, with 69% in favour and 26% against.

Labour voters are understandably less convinced, with 51% against and 40% in favour.

There is also a clear regional split: only 48% of people in the north of England and Scotland approve of the deal, against 68% in the south of England. Well-off voters are also much more enthusiastic than the less well-off.

Many people are also optimistic about the new government's prospects. Overall, 54% say they think it is likely to change Britain for the better, including 12% who say it is very likely to do so, and 41% disagree. Tories are keenest, with 87% saying the government will do the country good, compared with 62% of Lib Dems and only 28% of Labour voters.

Today's poll, carried out after the coalition government published its constitutional reform agenda last week, suggests voters may approve a referendum on a switch to the alternative vote. Even among Conservative supporters, only a narrow minority say they prefer first past the post.

Overall, 56% of voters are in favour of a more proportional system, even if it means more hung parliaments, while 38% are against. Lib Dem voters are most keen on the change, with 76% wanting to see a new system. Labour voters are also narrowly in favour, with 55% backing reform.

In a sign of possible future tension inside the coalition, slightly more Conservatives oppose change than support it. While 45% say they would like a new system, 49% say they want to stick with first past the post. But campaigners for electoral reform may draw comfort from the fact that opposition among Tory voters is not as high as among Tory MPs – almost all of whom are opposed.

ICM Research interviewed a random sample of 1,001 adults aged 18+ by telephone on 21-23 May 2010. 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.