David Cameron’s new MPs, the ones who won him a majority, are in a chipper mood as they head off for their first holiday after being elected. Some of them are surprised even to have won their seats, others are excited they’re in a fully Tory government. “My constituents wanted me to take full-blooded Toryism with me to Westminster,” one remarked to me recently. “And I’m surprised to be able to go back to them this summer and say I’m actually doing that.”

It’s nice these fresh-faced MPs are so happy. Many of their party colleagues working in Downing Street are also in fabulous moods, almost unable to believe their luck that they don’t have to nip across the office to ask a Lib Dem what they think, or stomp about to show their displeasure after reading newspapers full of negative briefings from coalition colleagues.

But while they’re entitled to celebrate life without the Lib Dems, are the Tories really right to be boasting about their “full-blooded Toryism”? After all, in the 10 weeks since winning that majority, the party has already retreated on three major issues: human rights, English votes and fox hunting. On the last there was a free vote, on which the Tory party was split. But with the other matters, the key problem was that not all of Mr Cameron’s 330 MPs were, in fact, so full-blooded in their support.

The Tory majority was a lovely surprise for the party, but it still hasn’t quite realised how unlovely governing with such a small number of MPs will be.

John Rentoul describes two-party politics as “more durable than fashionable opinion ever thought”. And, indeed, all that fuss during the election about the minor parties holding power seems a bit silly now. But look a little closer at the apparently healthy two-party system in Parliament, and you’ll see the Tories are actually rather anaemic.

The vote on English votes for English laws was pulled because a number of Conservative MPs were threatening to rebel, and because the Democratic Unionist Party said it wouldn’t support it either. (You don’t need many Tory MPs to start muttering about trotting through the wrong voting lobby to send the whips galloping in a panicked state to the DUP offices in Parliament.)

As it is, the DUP can offer only eight MPs to help out – but they could be lent upon because they are Mr Cameron’s only true allies in this Parliament. The SNP will only break their rule of not voting on English matters when they feel it will cause Mr Cameron a headache. The handful of remaining Lib Dems – now led by the left-wing, anti-coalition Tim Farron – want to avoid the Tories like the plague.

What does five more years of the Tories mean for Britain? Show all 8 1 /8 What does five more years of the Tories mean for Britain? What does five more years of the Tories mean for Britain? Welfare payments will be slashed One of the most controversial parts of the Conservative manifesto was to cut benefits for the working age poor by £12 bn over the next three years. But during the campaign they only said where £2 bn of these savings would come from. That leaves £10 bn still to find. Some experts think the only way they can close that gap is by means testing child benefit – with millions of families losing out Getty What does five more years of the Tories mean for Britain? There will be tax cuts for those in work and those who die The Tories will increase the threshold at which the 40p rate of tax becomes payable to £50,000 by 2020. They haven’t said so but it is also likely that at some point in the next five years they will abolish that 45p rate of tax altogether for the highest earners. They also want to increase the effective inheritance tax threshold for married couples and civil partners to £1m Getty What does five more years of the Tories mean for Britain? There will be an in/out EU referendum in 2017 The next two years are going to be dominated by the prospect of a referendum on Britain’s membership of the EU. First off David Cameron has the daunting task of negotiating a deal with other EU leaders an acceptable deal that he can sell to his party so he can go into the referendum campaigning for a ‘yes’ vote. This may be unachievable and it is possible that the Tories may end up arguing to leave. Opinion polls show Britain is divided on EU membership, one poll this year showed 51% said they would opt to leave compared to 49% who would vote to stay in Getty What does five more years of the Tories mean for Britain? There will be more privatisation of the NHS Having won the election the Tories now have a mandate to go further and faster reforming the NHS. In order to make cost savings there is likely to be greater private involvement in running services, while some smaller hospitals may lose services they currently provide like A&E and maternity units Getty What does five more years of the Tories mean for Britain? There will be many more free schools – and traditional state schools will become a thing of the past The Tories plans to create 500 new free schools and make 3,000 state schools become academies. They will also carry on reforming the Department of Education and remove more powers from local authorities over how schools are run Getty What does five more years of the Tories mean for Britain? On shore wind farms will be a thing of the past and fracking will be the future Government spending on renewable energy is under real threat now the Lib Dems are no longer in power with the Tories. Subsidies are likely to be slashed for off-shore wind farm and other green energy supplies. Meanwhile there will be generous tax break for fracking as ministers try and incentivise the industry to drill for onshore oil and gas Getty What does five more years of the Tories mean for Britain? There maybe more free childcare – but not necessarily In the campaign the Tories pledged to double the amount of free early education for three- and four-year-olds from 15 hours a week to 30. The extra hours would only be offered to working families where parents are employed for at least eight hours a week. However they have not said where the money will come from to fund the pledge Getty What does five more years of the Tories mean for Britain? Workers' rights could be reduced The Tories want to slash business regulation, merge regulator and cut costs. The Lib Dems stopped them from reducing the employment rights of workers in power – but these are now under threat Getty

Other smaller parties such as the Social Democratic and Labour Party, Plaid Cymru and the Greens rarely see eye to eye with Conservatives, while the Ulster Unionist Party only offer two MPs and don’t much like the Conservatives either, unless they’re offering a handsome deal. Ukip returned to parliament with just one MP, and one who was never particularly helpful to the Tory whips even when he was himself a Tory.

The DUP have a great deal of respect for Mark Harper, the Conservative chief whip, who has also impressed colleagues with his fair-minded efficiency and ability to tell Downing Street exactly how badly a campaign to get something through the Commons is going. But each time Harper and his colleagues come running to DUP chief whip Jeffrey Donaldson, they must make it worth his while to support a vote.

Of course the DUP only really comes into play when Tory MPs refuse to play ball. And just a few too many find trouble irresistible.

David Davis, for instance, played a key role in the decision to delay the vote on English votes until the autumn: one Cabinet minister describes him rather sourly as “a carrion crow hovering above the motorway”. Then there’s Andrew Mitchell, an opponent of human rights reforms who is asking increasingly troublesome questions.

The Tory whips group rebels according to whether they are sincere or “opportunists”. At present they can rely on the bulk of the party feeling cheerful and loyal, but as time wears on and more of those cheery new MPs are disappointed by reshuffles, then so the rebel group grows. And though the whips are working hard to stop embarrassing defeats by pulling votes, they are encouraging further bad behaviour in the long run. As one figure keen to exploit the party’s small majority says: “The more votes they pull out of, the more the rebels think they can get what they want.”