David Cameron is expected to hand new powers to the Scottish parliament to allow under-18s to vote, after an all-party deal last month.

The UK prime minister was due to confirm the new powers when he met Scotland’s first minister, Nicola Sturgeon, after a meeting of devolved and UK ministers in London on Monday.

Downing Street sources have indicated the powers could be fast-tracked to allow the change before the May 2016 Scottish elections.

More than 120,000 teenagers aged 16 and 17 were given the vote in the Scottish independence referendum for the first time. Electoral campaigners hailed the move as a success, with high levels of political engagement.

Proposals to allow the Scottish parliament to permanently extend the franchise were agreed by all the parties in the Smith commission talks on more powers for Holyrood last month.

That included the Conservatives, who have repeatedly resisted allowing 16- and 17-year-olds the vote in UK elections and English council elections, despite unanimous backing for the move by other parties.

Nick Clegg, the deputy prime minister, has suggested that a section 30 order will be used to modify the Scotland Act, the same mechanism that allowed Holyrood to stage the independence referendum, rather than introducing a wholly new act of parliament.

Speaking before Monday’s meeting with Cameron, Sturgeon had said she would press the prime minister for swift action on the voting measure.

“Giving 16- and 17-year-olds the vote for the independence referendum is widely seen as having been a huge success, which added to the unprecedented democratic engagement of the campaign and the massive turnout,” she said.

“We want to make sure those same young adults now have the chance to vote in the next Scottish parliament election, and have their say on how the country should be run.”