Lowering the voting age could be one of the first acts of a new Labour government as the party wants 16- and 17-year-olds to be able to vote in the London mayoral election of 2016, one of Ed Miliband's closest allies will say on Friday.

In a speech in London, Sadiq Khan, the shadow justice secretary, will say lowering the voting age is at the heart of the party's plans for constitutional reform.

Khan hopes to have legislation to change the voting age in place by the London mayoral contest of 2016, but the timing means a constitutional reform bill would have to be passed speedily to give young people time to register to vote.

Khan will argue that lowering the voting age is a crucial way of tackling "the public's malaise towards all things political".

The shadow justice secretary, who is tipped as a frontrunner to be Labour's candidate in the mayoral elections, will say: "I'd love it if we can get the law changed in time for the next London mayoral contest.

"Getting the public into the habit of voting is clearly a key part of any solution if we are to raise the numbers of those who participate in elections. We need to get people hooked on voting at an early age because the evidence shows if you vote when you first become eligible you're more likely to keep on voting for the rest of your life. Don't vote when you're young and you're more likely to never vote.

"Changing the law and extending those eligible to vote would mean governments in the future would be foolish to ignore their voice."

A Labour source said getting 16- and 17-year-olds to vote in 2016 is "our target".

Khan will confirm that the next Labour government will give 16- and 17-year-olds the vote during a conference at the IPPR thinktank, which has called in a policy paper to make voting compulsory for first-timers.

The shadow justice secretary will say: "A lot of work is going to need to be done if political parties are to re-connect with the public, and demonstrate they are relevant to the issues which affect people's lives on a day-to-day basis.

"The millions of ordinary voters who are involved in campaign groups and charities put political parties to shame, and shows the appetite for involvement is out there. But translating this into support for party politics is a challenge for everyone in Westminster, Cardiff, Edinburgh, Belfast and town halls up and down the country."

Labour also wants to tie up lowering the voting age with improved citizenship education in schools and putting polling stations in schools and colleges.

It comes after David Blunkett, the former Labour home secretary, called for politicians to do more to deal with the problem of voter apathy in the face of statistics showing only one in 10 young people were definitely planning to vote.

Earlier this week, the senior Labour MP said the issue was even more acute because the people turning off from politics were "the people who need political action and are dissuaded from doing so".

Blunkett particularly highlighted "devastating" figures from the Hansard Society showing as few at 12% of young people said they would be sure to vote in the general election.

The Guardian last month published ICM research showing that nearly half of Britons said they were angry with politics and politicians in a survey analysing the disconnection between British people and their democracy.

The research found that anger with the political class and broken promises made by high-profile figures most riled voters, rather than boredom with Westminster. The polling showed that ennui was more marked among the young, rivalling fury as the dominant feeling about politics among voters aged 18-24, who are evenly split 34%-34% between boredom and anger.

When Harold Wilson won the 1964 election, more than three quarters of people cast their vote and turnout was roughly equal across the generations. But according to data from Ipsos Mori, at the last election 76% of over-65s were still voting, while only 46% aged 18-24 were going to the ballot box.

The debate came to the fore when Russell Brand expressed the disaffection of many in October, telling Jeremy Paxman on Newsnight that he had never voted because he "can't be arsed", adding later: "The only reason to vote is if the vote represents power or change. I don't think it does."

After the interview, which received more than 10m hits on YouTube, Paxman said he understood Brand's decision, dubbing Westminster politics a "green-bench pantomime … a remote and self-important echo-chamber".