The drugs are designed to ensure that symptoms are mild and reduce the chance of an infected person giving the illness to someone else.
The UK has moved beyond the stage of containing swine flu into the "treatment phase", which means that Tamiflu is only being offered to people who have swine flu and not usually to their contacts.
While the latest study shows that antivirals can shorten the duration of normal seasonal flu in children by up to a day and a half, it also shows that they have little or no effect on asthma flare-ups, ear infections or the likelihood of children needing antibiotics.
But the drugs can cause unpleasant side effects, such as vomiting with Tamiflu.
ADVICE FOR PARENTS
Most cases of swine flu are relatively mild
Children sick with flu should have plenty of rest and fluids
Contact the child's doctor if their condition gets worse or there is cause for concern
A GP may prescribe Tamiflu, or patients can call the National Flu Service on 0800 1 513 100
There is also the risk that widespread use of the drugs will mean the virus will develop resistance to them.
For most children aged between 1 and 12, the risks associated with taking the drugs may well outweigh any benefits, say the researchers.
They say parents with sick children should make sure they get lots of rest and enough fluids and that they should contact their doctor if the child's condition gets worse.
In most cases, swine flu is a relatively mild disease.
Their work also reveals the effectiveness of using antivirals to contain the spread of flu.
They found that 13 people need to be treated to prevent one additional case, meaning antivirals reduce transmission by 8%.
BBC Health Correspondent Adam Brimelow
The government's flu pandemic plan has come under close and continuous scrutiny ever since the UK's first H1N1 swine flu cases were diagnosed three and a half months ago.
One of the biggest concerns has been the aggressive use of anti-viral drugs, drawing on a stockpile built up in advance to treat half the population, with further supplies still coming in.
The government has also lined up around a 130m vaccines, more than enough for everyone in the UK.
Over the last four years ministers have spent more than £500m on preparations for the pandemic.
So is this outlay proportionate to the risk? The total of swine flu related deaths so far across the UK is 41.
Seasonal flu routinely kills 12,000 people in England and Wales each year, without provoking anything like the same response.
But it is important to remember we are still in the first wave of swine flu. The situation in the autumn may be much worse.
For now ministers and their advisers are prepared to err on the side of caution even if that means people having Tamiflu who do not need it.
They say they will be guided in their decisions by science.
However, a lot of the evidence on swine flu is still emerging so they will continue to rely on a safety-first approach.
The University of Oxford team, led by Dr Matthew Thompson, carried out a review of four trials on the treatment of seasonal flu in 1,766 children and three trials involving the use of antiviral to limit the spread of seasonal flu in 863 children.
Dr Thompson said: "Our research is finding for most children these antiviral drugs are probably not going to have much of an effect."
Co-researcher Dr Carl Heneghan, a GP and clinical lecturer at Oxford University, said the current policy of giving Tamiflu for mild illness was an "inappropriate strategy".
He said: "The downside of the harms outweigh the one-day reduction in symptomatic benefits."
Flu expert Professor Hugh Pennington said the findings were not surprising and underlined what was already known about Tamiflu.
"Tamiflu has a place but it's not a wonder cure."
A Department of Health spokesman said: "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.
"The BMJ research is correct to say that many people with swine flu only get mild symptoms, and they may find bed rest and over-the-counter flu remedies work for them.
"But 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."
Liberal Democrat Shadow Health Secretary Norman Lamb called for an urgent review of the policy.
But Professor Steve Field, chairman of the Royal College of GPs, said the current policy was correct.
The Royal College of Paediatrics and Child Health also supports the Department of Health advice.
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