The recommendation by a cross group party of MPs on the House of Commons' home affairs select committee has been described as a "huge step backwards" by Peter Saunders who runs the National Association of People Abused in Childhood (NAPAC).
"When a name is put out there it gives other alleged victims the potential to come forward and to make their voice heard and to corroborate and potentially be a witness in such a trial," said Peter Saunders in an interview with Premier.
"Very few people who are arrested and questioned over these crimes, very few of them will ever make it into the newspapers, let alone the headlines," Mr Saunders added.
The committee wants to see the media banned from naming suspects, such as Sir Cliff Richard, unless and until they are charged with an offence.
MPs were given evidence about the media coverage of last year's police search of Sir Cliff Richard's home after details were leaked to the media. He's subsequently complained to police and no charges were made.
They also heard from the Leveson inquiry on the media impact of leaking the name of Christopher Jefferies, who was wrongly linked to the murder of Joanna Yeates in Bristol.
The committee's report says an initial 28-day time limit should also be introduced on police bail, with extensions needing to be signed off by senior officers and a court review every three months.
