Smith has vowed that his Labour MPs would seek to block the Prime Minister triggering formal Brexit procedures if he is named party leader next month.
The Labour leadership challenger said failing to take Brexit back to the people amounted to writing the government “a blank cheque” on a talks with the EU.
"Theresa May says that 'Brexit means Brexit' – but nobody knows what Brexit looks like,” Smith said.
“It could involve trashing workers' rights and environmental protections, opening our NHS up to foreign competition, making it harder for us to trade with our neighbours and damaging our economy.”
It comes two months to the day after the UK's decision to leave the EU was announced, and Conservative MP Kwasi Kwarteng said the move reflected a party ignoring its traditional voters. One in three Labour voters is estimated to have backed Brexit.
“For these guys to think that they can reverse this when their heartlands have spoken loud and clear is just an invitation to appeal to that electoral base,” Kwarteng said.