McLaren was born in Edinburgh before moving to Livingston and then West Calder, where she spent most of her childhood. Her great grandfather was a shale miner and a member of the Independent Labour Party in West Calder. Her father was a member of the Communist Party of Great Britain and later Democratic Left Scotland. Her mother is a former member of the Socialist Workers Party. Her family were activists for a "Yes, Yes" vote in the 1979 referendum on Scottish devolution.