AS the Scottish National Party MPs settled themselves into "Freedom Alley", as the former LibDem corridor in the Commons is now called, there has been a sense of optimism.

They are the third party in the UK and and will be a welcome breath of fresh air in the stuffy corridors of power. But no-one is saying it will be easy.

This is shaping up as the most right-wing Conservative government since 1979 when Margaret Thatcher took over from the ruins of the Callaghan administration. As happened then, Labour has retreated into a period of self-doubt and division and seems eager to turn the clock back to the days of New Labour.

This means that Labour may be in no position to provide vigorous opposition to the Tory policies on welfare, privatisation, immigration, human rights and protection of trades unions. In fact, if the followers of Tony Blair get their way, we might hear its spokespeople promising - as Rachel Reeves did last year - to be tougher on benefits policy than the Tories. The UK party may also support new anti-terror laws and be relaxed about market reforms in the NHS.

Worryingly, there aren't even the moderating voices any longer in the Conservative Party - the "wets" as they used to be called in Thatcher's day, such as George Younger and Jim Prior - who offered some kind of a check on the ambitions of the right. It's not that kind of Tory Party any more.

Part of the problem is that the Conservatives never really expected to win an outright majority. They probably assumed that some of the harder edges of their policies would be rubbed off in coalition talks with the Liberal Democrats. But they are now off the leash.

The manifesto pledge to outlaw increases in income tax, national insurance and VAT will presumably be implemented even though this could force still deeper cuts in public spending.

The promise to introduce "English votes for English laws" will have to be honoured somehow, though the Scottish MPs will oppose any attempts to exclude them from nominally "English" legislation, such as tax changes in the Budget, that have a financial impact in Scotland.

David Cameron has made his intentions regarding Scotland pretty clear by installing Margaret Thatcher's former poll tax adviser, Andrew Dunlop, as a minister in the Scotland Office. Dunlop isn't an MP, so he had to be ennobled first. Installing an unelected right-wing peer in the "government in exile" in the Scotland Office is a red rag to the SNP, and Cameron knows. it.

I tweeted in jest last Thursday that he was about to ennoble the Scottish businesswoman Michelle Mone (who said she would leave if Scotland voted Yes) to join the Scotland Office team. Not a few people took it seriously. Such are the times.

The first encounter between Nicola Sturgeon and David Cameron on Friday however was all very diplomatic. Neither side wants to go to war right now, and the FM was keen to ramp down speculation in the press that she was threatening an early referendum if she didn't get progress to full fiscal autonomy.

This was always fantasy. Sturgeon has made clear she is not planning an early referendum. This is for the very obvious reason that she'd probably lose it. The SNP may have won a landslide but it only returned 50% of the popular vote and many of those voted No in the last referendum.

Cameron said he was prepared to consider strengthening the welfare proposals in the bill to implement the Smith Commission agreement, which will involve the Scottish Parliament adjusting benefit levels. The Scottish Government also wants powers on employment, National Insurance, minimum wage and equality legislation.

But there seems little prospect now of the Scottish Parliament being given the kind of latitude on welfare that the First Minister wants. The Conservatives have pledged to make a further £12bn a year in cuts to the welfare budget. We're talking deep cuts here - not just freezing benefits below inflation and imposing a £23,000 cap.

The PM has reinstated the much-criticised Iain Duncan Smith as Work and Pensions Secretary. He will press ahead with his plans for Universal Credit to replace the range of benefits including Housing Benefit.

The bedroom tax will stay, in England at least, as will the sanctions regime that charities say is to blame for the increase in the use of food banks. There is not a great deal the SNP MPs can do about this since welfare is not devolved.

They may have more success in delaying or scrapping the Government's plan to abolish the Human Rights Act (HRA). This would plunge the UK Government into a legal tussle with Holyrood over the Sewel Convention, which says that the Scottish Parliament must agree acts of the UK Parliament that cut across its legislative competence. The HRA is effectively written into the Scotland Act.

There is a degree of urgency about this because the Home Secretary is proposing a range of new anti-terror laws. Theresa May gave a lamentable performance on the BBC's Today programme last week trying to explain what exactly she intended to make illegal. There are already plenty of laws against incitement to racial hatred or terrorism.

But the Prime Minister is determined. He came out with the extraordinary proposition last week that Britain had been too "passively tolerant" of people who remained within the law but encouraged terror. His message appeared to be: don't think you can escape the law simply by obeying it.

The SNP is a party which has been accused of spreading "anger, fear and division" itself - not least by Labour leadership contender Yvette Cooper last week. It should make its opposition to this clear.

Nicola Sturgeon has also said that the EU referendum could be the kind of "material change" that justifies another independence referendum. However, it is going to be difficult to argue that the UK has no right to hold a referendum on its constitutional destiny only a year after Scotland had done precisely that.

The FM hopes to enlist the Irish and Welsh parliaments in a bid to claim that it would be unconstitutional for Britain to leave the EU if the "family of nations" of the UK do not all give their assent. One slight presentational problem here is that the SNP and Cameron are likely to find themselves tactically on the same side in the referendum campaign since it is expected that the PM will argue for Britain to stay in the EU.

The BBC is another case in which the SNP might find itself speaking with two voices. It will oppose the new culture minister, John Whittingdale, in his war against the BBC. The SNP supports the idea of public service broadcasting and wants the licence fee retained. But there are many in the party who would like to see the BBC's wings clipped on account of its coverage of the independence referendum campaign.

The chair of Yes Scotland, Blair Jenkins, said he didn't think the BBC was structurally biased, though there were problems with the coverage. But the SNP MPs will have to ensure that their enmity toward the BBC does not put them by default in the same camp as those who would like to see the BBC diminished as an institution.

That is not the kind of opposition Scotland needs right now. It is fine to argue for the devolution of broadcasting to Holyrood - a curious anomaly since responsibility for the press is devolved. But curbing the BBC will only give comfort to the conservative UK press.

After their success in demonising Ed Miliband and Nicola Sturgeon during the General Election, the non-dom dominated press are hell-bent on pressing Cameron to turn Britain into the most pitiless right wing-nation in Europe.