The leader of the Scottish National party at Westminster has suggested that the people of Scotland could vote to leave the UK in a second independence referendum within five years if David Cameron fails to deliver on promises for greater devolution and imposes more austerity north of the border.

In an interview with the Observer, Angus Robertson, who leads 56 SNP MPs in the House of Commons – in what is now the third largest party – said many politicians at Westminster had clearly failed to grasp the scale of the political change in Scotland. The Tory government, he claimed, was attempting to backtrack on promises, made before and after last year’s independence referendum, to devolve more powers to Scotland while preparing an austerity budget that would also further inflame resentment. Some in the UK parliament, he said, seemed to be living in the vain hope that the SNP, and the pressure for independence, were temporary phenomena which would just “go away” – something he insisted would not happen.

The clearest sign of Westminster’s failure to comprehend the SNP and the wishes of Scots, he said, was the content of the Scotland bill on devolving powers which, as currently drafted, failed to implement many of the recommendations of the Smith commission that Cameron had pledged to introduce in full. Signs of backtracking by the government were feeding resentment among the Scottish people, who felt increasingly that Westminster was ignoring their wishes and failing to take on board the lessons from the SNP landslide north of the border.

Asked whether he believed there could be a second referendum and a Yes vote before the end of Cameron’s second term, Robertson refused to rule out the possibility. “I think that largely lies with David Cameron. He has to make a decision as to how he is going to approach governing Scotland with only one MP, having made a cast-iron promise and an undertaking to deliver on more powers for the Scottish parliament and the voters.”

He added: “Do I believe that in the future there will be further moves towards Scottish self-government? Yes, I do. Do I believe that there will in time be a growing desire in Scotland for independence? Yes, I do. Do I believe that in time there will be a referendum when the public wants it on independence and that there will be a Yes result? Yes, I do.”

Robertson insists his MPs are working constructively in parliament, but maintains the other parties are finding it impossible to accept the new force in their midst. “Westminster is having to come to terms with a very changed position in the chamber, where the Liberal Democrats are hard to see or hear because there are so few of them and this massive cohort of SNP are shocking the system by turning up to debates and taking part and having views that parts of the political class at Westminster have never heard.

“Images are regularly tweeted in Scotland of the small number of Tories on one side [of the House of Commons]and a similarly small number of Labour MPs – and scores of SNP MPs filling up the benches of the third party. Our party has arrived here with a job to do and, boy, are they going to do it.”

The SNP task was clear. “We were elected on a very well understood platform, standing up for Scottish interests to deliver the new powers that were promised to voters who voted both Yes and No in the referendum last year. We were elected on a strong mandate to oppose austerity, to resist the renewal of Trident, to represent our constituents. Unlike other parties, we have an extremely tangible north star.”

The SNP says it fully respects the narrow No vote last year, and that it is up to the Scottish people to decide if and when they want another independence referendum, an option party leader Nicola Sturgeon has refused to fully close off. There has been speculation that plans for one could be included in some form in the SNP manifesto for the Holyrood elections next year.

In the meantime the party is portraying the government and Westminster parties as serial betrayers. Robertson say that a cross-party report by the Scottish parliament, as well as analysis by the House of Commons Library, supports its view that the Scotland bill falls short of the recommendations made by the Smith commission, a claim the government strongly rejects.

Cameron says the bill does implement the commission’s recommendations and argues that the SNP is now backing off from its previous demands for full fiscal autonomy because it has realised it would be a bad deal for Scotland.

On devolution, Robertson added: “A promise was made and already we can see with the government’s legislation in the Scotland bill that has been presented does not match the Smith commission that was agreed and does not match the commitment made by the PM that he would look seriously on the proposals from the Scottish government on further devolution, which is what the people of Scotland voted on at the general election.”

The SNP says the bill fails to guarantee greater powers over welfare payments, and goes nowhere near delivering on Cameron’s pledge for a redistribution of power that would be as “close to federalism as possible”.

Ahead of next month’s budget, he said Scots would not take kindly to a package that imposed further cuts on them, in the form of £12bn of welfare reductions. Plans for a proposed multibillion pound renovation of parliament – which the SNP believes will rekindle memories of the fiasco of a Scottish parliament building completed three years late and at 10 times the original budget – were also unacceptable.

“Of course one needs to make sure a public building can function for its purpose, but spending £5bn, £8bn, £12bn on a renovation project I think is going to find very little favour with people who are about to be told their income is about to be cut very severely. There is hardly a bigger example of wrong priorities.

“The more that the UK parties, having been humiliated in the general election, do not respect the voters who voted for the SNP in the general election – but not for independence – there will be a growing view in Scotland that political institutions are not in a position to understand or care enough to realise that change needs to happen.”