12 August 2016 Last updated at 11:51 BST
The report was commissioned by former PM David Cameron in the wake of the Tower Hamlets election fraud scandal in 2015.
He said the review had heard evidence that in a London borough at the general election someone arrived at the polling station with 500 postal votes.
"I'm very worried - I don't believe political parties should touch or handle in any way a completed ballot paper," he said.
Former communities secretary Sir Eric Pickles has told the BBC about his concerns over the findings of his report on tackling electoral fraud.