Labour's Twigg and Green, a Liberal Democrat, must now give up their roles on the council after being ousted from Parliament by the Conservatives.
Clare Oliver, the council's head of policy, described both men as "fantastic advocates for young people".
Twigg, the schools minister, had represented Enfield Southgate since 1997 and was defeated by 1,747 votes. Green, who lost his Ludlow seat by 2,027 votes, was Lib Dem spokesman on youth issues and vice-chairman of the All-Party Parliamentary Group on Youth Affairs.
Green said reducing the voting age was one of the issues he had fought hardest on during his three years as Lib Dem youth spokesman. He said of his defeat: "It's probably a bad thing for young people because I'm pretty certain that I got a lot of young people's votes.
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