Alex Salmond has been given the green light by David Cameron to pursue a referendum on Scottish independence after the first minister swept back into power with a commanding majority in the Scottish parliament.

The prime minister spoke to Salmond hours after the Scottish National party won a dramatic victory in the Holyrood elections, and guaranteed that the UK government would not put any legal or political obstacles in the way of an independence referendum.

Ministers in London will also speed up the introduction of new borrowing powers for Holyrood, which will be worth at least £2bn, and allow communities in Scotland to earn more money from charges on offshore green energy projects currently paid to the Crown Estates.

Cameron's concessions finally clear away any prospect of the UK government challenging the legality of a referendum: senior figures in the last Labour government believed a referendum was barred under the Scotland Act because changes to the British constitution are the preserve of Westminster.

Michael Moore, the Scottish secretary, said: "As a government, at a UK level, we won't put obstacles in their path." He added: "It entirely depends on how this is structured. The prime minister was entirely clear with the first minister yesterday: we will not stand in the way of this happening."

Moore chose his words carefully, admitting that, as a Liberal Democrat MP, he would join with Cameron in campaigning vigorously against independence.

Salmond indicated he had no plans to speed up his intention of staging the referendum in the latter half of the new SNP government's five-year term. Speaking outside Holyrood after he posed for a photocall with the SNP's 69 MSPs, he said Cameron's decision was "inevitable" but his government would stick firmly to the timetable set out in the election campaign, and resist pressure to call an early referendum.

As Salmond was embracing his new colleagues, many of whom never expected to be elected, it emerged that Tavish Scott had resigned as leader of the Scottish Liberal Democrats with immediate effect after the party was humiliated in Thursday's elections.

The party was reduced to four MSPs, leaving it the second smallest at Holyrood after voters punished it for forming the coalition with the Tories at Westminster. Scott said the result had been disastrous. "I must and do take responsibility for the verdict of the electorate," he added. "The party needs a new direction, new thinking and new leadership to win back the trust of the Scottish people."

Salmond said he had told Cameron by telephone on Friday night that his first priority was to put "economic teeth" on the amendments to the Scotland Act now going through Westminster. As a halfway measure before pressing for independence, Salmond wants to increase Holyrood's borrowing powers to £5bn.

• The following correction was printed in the Observer's For the Record column, Sunday 15 May 2011. This article said the Lib Dems in Scotland were reduced to four MSPs. Five, actually.