David Cameron is risking a “double betrayal” of Scotland if his government fails to make urgent changes to the Scotland bill, Gordon Brown has warned.

The former Labour prime minister said the package of new powers for Holyrood must be amended to give MSPs unconditional authority to top up welfare payments, without any risk of such decisions being vetoed by the UK government.

He said such changes were necessary to fulfil the pledge of more powers made by Westminster before last year’s independence referendum and to deliver in full on the recommendations of the Smith commission, which the prime minister set up to carry out a review of devolution.

Brown, who was addressing an audience at Glasgow University, said that with the Scotland bill due to to be debated by MPs in two weeks, there was an “urgent requirement” for action.

The former Labour leader, who was instrumental in drawing up the promise of more powers for Holyrood last September, said the Smith commission had recommended a number of changes in the way Scotland was governed.

These included top-up powers on welfare, with Brown saying: “In other words, if a decision was made by the UK government on tax credits, about child benefit or benefits for the unemployed, and the Scottish parliament did not like that decision, it would have the power if it so wished, and if it was prepared to pay for it, to top up these benefits.”

But he added: “When we saw the Scotland bill a few months ago, it was clear that there was not an unconditional devolution of powers to top up welfare. There was no clear and unambiguous right to top up welfare. And when the Scotland bill was published it also suggested that there may be conditions or caveats that were placed on the Scottish parliament if it did wish to top up welfare.

“In other words, if it wanted to ask the Department for Work and Pensions to raise tax credits or raise child benefit, the Department for Work and Pensions may have had the power to say: ‘We can’t do this, this is not possible administratively’ and that might be the end of the matter.”

The Scottish secretary, David Mundell, has already pledged to bring forward “substantive amendments” to the bill in the next two to three weeks.

Brown argued that it was “absolutely essential” for the legislation to be altered to give Holyrood “this top-up power on welfare” and for the “removal of any doubt as to whether there is a veto power on welfare powers”.

The former prime minister, who has written to the Cameron on the issue, said: “I hope in the next few days, because we’ve only got two weeks to go before this is debated in the House of Commons, the government will see sense and make the change that is essential.”

The shadow Scottish secretary, Ian Murray, has put forward amendments to make the changes. Brown said: “In the next few days, the government has a choice either to make these changes or to be accused of failing to implement the Smith recommendations and to be accused of what might be seen as a a double betrayal of the people of Scotland, that they are not implementing the Smith recommendations, and they are preventing the Scottish parliament being able to do something about poverty.”

The former prime minister said “almost certainly the most controversial set of decisions that are being made that will affect Scotland and the rest of Britain in the next few years are on welfare”, claiming that changes to tax credits could see families lose up to £3,000 a year.

“Without these new powers the Scottish parliament would be unable to do anything about it. Without these powers we would not be implementing the Smith recommendations in full,” he said.

“There are two reasons why we need to make a change to the Scotland bill. One is to keep the promise that was made last September, and the promise that was made in the recommendations of the Smith commission.

“And the second is that we have to be able to deal with these oncoming problems of poverty and the impact of what is called the policy of austerity. But with these powers we would be able to say that the Smith recommendations have been delivered. With these powers we would be able to say that the vow that was made last September had been upheld.”