Despite public harmony, coalition parties remain divided

Frantic behind-the-scenes negotiations are taking place to resolve policy differences between the Conservatives and Liberal Democrats before the coalition government outlines its legislative programme next week.

In public, the two partners are managing to maintain a united front. In private, there is some hard bargaining between Tory and Liberal Democrat ministers as they try to square the circle before the Queen's Speech next Tuesday.

"We are paddling like hell beneath the surface," one Tory insider admitted. The coalition's first agreement, launched by the Prime Minister and his deputy in Downing Street's Rose Garden last week, resolved some thorny issues but put off other battles to another day. A second joint policy document will be published in the next few days and will answer some – if not all – of the outstanding questions.

Yesterday Mr Cameron told the Cabinet at its second meeting since the election that agreement on the Queen's Speech would be the "main focus" of this week.

Right-wing Tory MPs fear their party's plans to replace the Human Rights Act with a UK Bill of Rights will bite the dust. Mr Clegg's party strongly supports the Act and both Kenneth Clarke, the Justice Secretary, and Dominic Grieve, the Attorney General, are said to be lukewarm about wide-ranging reform. The Act may be reviewed by a commission, which will be seen as a way of delaying reform – and possibly doing nothing.

Sentencing and prisons policy are a likely source of tension between the coalition partners. At the election, the Tories argued that people convicted of knife crimes should face a jail term and attacked Liberal Democrat proposals to bring in a presumption against prison sentences of less than six months. The Tories wanted to redevelop the prison estate and halt early release, while the Liberal Democrats wanted to cancel the prison building programme.

There is also anxiety among Tory MPs about plans to raise the rate of capital gains tax from 18 to 40 per cent, a Liberal Democrat demand which would hit people selling shares and second homes. George Osborne, the Chancellor, has backed reform to prevent people escaping higher tax payments but has asked Treasury officials to draw up a range of options.

Pressure groups representing the elderly are pressing for an early statement on social care, which is one of the biggest challenges facing the Government. The Tories favour allowing people to pay a one-off insurance premium of about £8,000 to avoid having to sell their home to pay for residential care. The Liberal Democrats, who were closer to Labour than the Tories on the issue before the election, called for an independent commission.

Tory MPs will be watching the Queen's Speech closely to see whether the party's pledge to offer a free vote on lifting the ban on hunting with dogs will go ahead. This was promised in opposition by Nick Herbert, the pro-hunting former shadow Environment Secretary. But Tory backbenchers saw it as an ominous sign when Mr Herbert did not become Environment Secretary and instead had to settle for a non-Cabinet post as Police Minister.

Other tricky issues may be also kicked into the long grass. Vince Cable, the Liberal Democrat Business Secretary, wants a split between the banks' high street and investment operations. But Mr Osborne is in the driving seat and the Treasury is anxious to maximise the proceeds from the sale of the state's share in the Royal Bank of Scotland and the Lloyds Banking Group. Again, a commission will investigate the future of the banks.

In other areas, the two coalition partners have agreed to disagree. Liberal Democrat MPs will not have to vote for a new generation of nuclear power stations, which will go ahead only if there is no public subsidy, or for Tory plans to reward marriage in the tax system, which Tory ministers hope will sneak through if the Liberal Democrats abstain.

The Liberal Democrats will be free to make the case for alternatives to a like-for-like replacement for Britain's Trident nuclear missile system, which they opposed at the election. And they will not have to support a rise in university tuition fees if, as expected, this is recommended by a review of higher education funding. The Liberal Democrat manifesto pledged to phase out the fees in six years.

POINTS OF DIFFERENCE...

Human Rights Act Tory plans to replace it may be kicked into touch by Kenneth Clarke, the Justice Secretary,who in 2006 dismissed David Cameron's proposals for a UK Bill of Rights as "xenophobic" and "anti-foreigner"

Social care Will Liberal Democrats back Tory plans for an £8,000 one-off insurance premium to prevent sale of people's homes to meet their residential care fees?

Fox hunting Liberal Democrats may try to delay Tory plans for a free Commons vote which could lead to lifting of Labour's ban on hunting with dogs

Capital Gains Tax (CGT) Tory backbenchers are nervous that the party's natural supporters will be hit by Liberal Democrat plans to raise CGT from 18 to 40 per cent on the sale of second homes and shares

Banks George Osborne, the Chancellor, and Vince Cable, the Business Secretary, are on a possible collision course over whether banks' retail and investment functions should be split up

Sentencing Tories attacked Liberal Democrats' "soft" stance on early release during the election, claiming 60,000 offenders would walk free

Prison-building Liberal Democrats want the prison-building programme scrapped in order to make savings of £795m next year but Tories want to expand it to halt the early-release scheme