Suspects in sex cases should be granted the protection of anonymity until they are formally charged, an influential group of MPs has recommended.
Mr Kelly's case was mentioned by peers
Under current laws, the complainant is entitled to anonymity, but since 1988 it has been possible to name the accused - who have included some high profile personalities.
Now the Commons home affairs committee, reporting on the Sexual Offences Bill, says the names of those accused of rape and other sexual offences should not be released unless and until charges are made.
The government's far-reaching attempt to reform sexual offences is due for debate in the Commons next Tuesday.
In the committee's report, it raises the case of television presenter Matthew Kelly, who was questioned over alleged child sex abuse offences earlier this year.
Following a police investigation the inquiry was dropped, and Mr Kelly's name was cleared.
But during the month in which the complaint was investigated, Mr Kelly had been subjected to intense media scrutiny.
The Home Office said it was "not minded" to follow the recommendations, saying there was "no justification for extending the protection of anonymity to those suspected of a sexual offence".
"We appreciate the very great distress that is often experienced by those
wrongly accused or charged with a sexual offence after having been publicly
identified," he said.
The Hamiltons were accused in a blaze of publicity
"However, the criminal justice system operates on a principle of openness,
which is a vital ingredient in maintaining public confidence and encouraging
witnesses to come forward.
"We do not believe there is any justification for
those accused of sexual offences to be singled out for special protection while
other defendants, including those accused of murder, could be identified."
The Home Office is currently in talks with the police and the newspaper industry to see what can be done to strengthen guidelines about disclosure and reporting of the names of people being investigated.
Former Conservative MP Neil Hamilton and his wife Christine called for a change in the law after they were falsely accused of rape by Nadine Milroy-Sloan.
The Hamiltons, who were initially arrested after the accusation was made, were cleared of any involvement and Milroy-Sloan was found guilty of making up the incident.
Milroy-Sloan, who was described as a "fantasist" in court, was jailed last month for perverting the course of justice.
Mr Hamilton told BBC News "fuel was added to the flames" when Milroy-Sloan "sold her anonymity" to the News of the World newspaper.
"That would not have happened if we had not been identifiable," he said.
The home affairs committee also recommended that having sex in public toilets should remain a criminal offence.
They called for an amendment to the Public Order Act, stating that its prohibition of "threatening, abusive or insulting behaviour" should include "cottaging".
The practice is currently illegal under laws on buggery and gross indecency, but these are being repealed by the Sexual Offences Bill.
Last month the House of Lords voted to amend the bill to say anyone caught cottaging should face prosecution and jail terms of up to two years, but the Home Office said the change would make the bill unworkable.
"There is much concern and disagreement as to whether this bill will legalise sexual activity in public toilets," the committee said.
"We recommend that sexual activity in public toilets should be a criminal
offence and suggest that this could be dealt with by an amendment to section 5 of the Public Order Act 1986, which makes it clear that 'insulting' behaviour
includes sexual behaviour.
"This would dispense of the need to prove specific sexual acts and also has
the advantage of empowering the police to give a warning before making an
A Home Office spokesman said he agreed that the Public Order Act was "capable of covering sexual activity in a public toilet where this causes outrage or offence".
The Home Office was "considering the way forward" on the Lords' amendment on sex in public toilets.