Mr Shelbrooke is backing a campaign spearheaded by Pamela Whitlam, whose 11-year-old son Harry of East Ardsley died after he was struck by a reversing tractor at Swithens Farm in Rothwell in August 2013.
Tractor driver Gary Green was over the drink drive limit but could not be prosecuted under road traffic laws because it happened on private land.
Green, of Wakefield, was jailed for 16 months and two weeks for health and safety violations which contributed to Harry’s death.
Campaigners want Whitlam’s Law to end the anomaly that drink-driving laws apply only to vehicles driven on public land. Transport Minsiter John Hayes said he was willing to meet Pamela Whitlam and Mr Shelbrooke following a debate in the Commons last month. A spokesman for Switalskis Solicitors, who represent Pamela Whitlam, said: “Alec will submit a formal request for a meeting, likely to be in Whitehall around late October or early November.”