Vomiting is more dangerous in children than in adults as it can rapidly lead to dehydration and admission to hospital, they said.
Also the drugs had little or no effect on asthma flare-ups, ear infections or the likelihood of a child needing antibiotics meaning on balance the medicine does more harm than good in otherwise healthy children, the authors said.
It comes after research last week showed that Tamiflu reduced the length of flu in adults by just half a day.
Together the findings will question whether the Government's policy of stockpiling enough antiviral drugs for 80 per cent of the population was a waste of money. The exact cost of the stockpile has been kept secret for 'commercial reasons' but is expected to run to tens of millions of pounds.
Countries around the world have stockpiled around 50m doses of Tamiflu, made by Roche, for use during a flu pandemic.
Tamiflu has also been linked to side effects such as insomnia and nightmares in children.
Dr Matthew Thompson, a GP and senior clinical scientist at Oxford University and Dr Carl Heneghan, a clinical lecturer at Oxford University, said the findings review of seven research studies should prompt the Department of Health to reconsider its policy.
The study, published online in the British Medical Journal, reviewed trials where children aged between one and 12 were either given Relenza or Tamiflu to treat seasonal flu or where one of their family had flu and they were given medicine to stop them becoming ill.
The researchers said although the studies were carried out on seasonal flu the findings are relevant to the current swine flu outbreak.
The drugs may still be of some benefit for children who have underlying conditions such as cystic fibrosis or whose immune system is compromised because they are being treated for leukaemia, for example, but there was not enough evidence to be conclusive about this, the researchers said.
Dr Thompson said the Government's current policy of giving Tamiflu to all symptomatic people was 'inappropriate'.
GPs are using their clinical judgement and providing anti-virals to severe cases of flu but the National Pandemic Flu Service is handing out the drugs to anyone who fits the criteria for having a flu-like illness. Data from the Health Protection Agency has suggested only one in four of those with symptoms will actually have swine flu.
The Flu Service handed out 150,000 doses of Tamiflu in its first week as cases peaked at around 110,000 in seven days.
Dr Thompson said: "Reserving these antiviral drugs for children who are more likely to have complications may be a more sensible strategy and would take some of the pressure off the current public demand for anti-virals."
Dr Heneghan warned that prescribing the drugs so widely will encourage flu to become resistant to the medicine.
He said: "Going forward we have a treatment which is ineffective because we've given it to everybody."
He also warned that people were relying on Tamiflu, 'like a magic bullet', and this meant that serious complications of swine flu could be dismissed in those on the drug.
Parents should treat flu in children with paracetamol and rest but watch carefully for complications and contact their GP if they are worried, the authors said.
The research trials which were reviewed have been available for over a year and the Government could have carried out its own study in this before the outbreak of swine flu began, they said.
The findings also showed that when using antiviral drugs in children who have been exposed to flu but do not yet have symptoms, as preventive treatment, they were of limited use. They found 13 children need to be treated to prevent one case, meaning onward transmission was only reduced by eight per cent.
Government data released on July 30th suggested that by then one in 77 children aged between one and four had already had swine flu along with one in 95 of those aged between four and 14.
Norman Lamb, Liberal Democrat health spokesman said: "An urgent review must be carried out into whether the benefits of prescribing certain antiviral drugs are worth the risks when it comes to our children’s health.
“Parents will now need urgent guidance and reassurance about what exactly they should be doing to look after their children. This is even more crucial given that health experts are predicting a surge in swine flu cases this autumn.”
A Department of Health spokesman said: "The BMJ review is based on seasonal flu and not swine flu. As the authors note, the extent to which the findings can be applied to the current pandemic is questionable - after all, we already know that swine flu behaves differently to seasonal flu, and past pandemics have hit younger people hardest.
"Whilst there is doubt about how swine flu affects children, we believe a safety-first approach of offering antivirals to everyone remains a sensible and responsible way forward. However, we will keep this policy under review as we learn more about the virus and its effects.
"For those who experience severe symptoms, the best scientific advice tells us that Tamiflu should still be taken as soon as possible - and to suggest otherwise is potentially dangerous.
"If people are in any doubt about whether to take Tamiflu, they should contact their GP."
The latest figures have suggested the first wave of the swine flu outbreak has peaked with officials saying around 30,000 new cases were diagnosed in the week ending August 1st but a second wave it still expected later in the autumn.
So far 36 people with swine flu have died.