Turner's comments add to a growing Labour opposition to the plan.
Six Labour MPs, including former shadow chancellor John McDonnell, signed Turner's Commons motion against the plans.
Several other prominent left-wingers have criticised the plans publicly.
On Wednesday, Labour MP for Clapham Bell Ribeiro-Addy said "scrapping jury trials would undermine a foundational principle of British justice: the right to have your case heard by fellow citizens."
"We need investment and reform to tackle court backlogs, not the abolition of key legal safeguards," she added.
Responding to Lammy's Commons statement, Labour MP for Walthamstow Stella Creasy said it was "hard to see how" the plan would "address that backlog" given jury trials only accounted for 3% of cases.
In the same debate, Labour's Eltham and Chislehurst MP Clive Efford warned the changes could penalise working-class defendants and create "'us' and 'them' in the criminal justice system.
Richard Burgon, the MP for Leeds East, said the policy sent "a chill through my heart".