Universal vaccination of all children aged six months to five years would cut the number presenting with lower respiratory infections, they said.
Professor David Mant and colleague consultant epidemiologist Richard Mayon-White wrote in a British Journal of General Practice (BJGP) editorial that the associated drop in consultations would balance out the extra workload to vaccinate millions of children in this age group.
The RCGP backed the calls, saying vaccinating all young children was 'a must'.
In 2008/9, less than a quarter of at-risk patients aged 2-16 years were vaccinated against flu.
Vaccination in this age group was also low during the 2009/10 flu pandemic.
Yet uptake among people over 65 remains high at about 72% in England.
A study led by Inverness GP Dr Rod Sampson, published in the same issue of the BJGP, revealed that common concerns from parents on vaccine safety, side effects and necessity may have kept uptake rates low.
A blanket vaccination policy should be implemented for this age group because selective policy has not worked, the editorial concluded.
‘Parental anxiety about the safety and effectiveness of vaccines in general should be addressed by an enhanced public education programme, supported by the media,’ they wrote.
'Parents need to understand that children are not being "over-vaccinated" and that immunisation is the safest and most effective medical intervention provided by the NHS.’
The authors admitted the additional workload incurred by such a switch ‘is not trivial’.
But this would be offset by a reduction in consultations for lower respirator illness of about 20%, they argued, and may also reduce inappropriate antibiotic prescribing.
RCGP immunisation spokesman and Berkshire GP Dr George Kassianos said: 'By immunising young children, we not only protect them from influenza infection but we also protect the elderly by creating herd immunity.'
He added: 'UK general practice has the capacity and the willingness to immunise children against influenza provided there was to be a sustained campaign by the DoH to inform and educate parents about the benefits of such influenza immunisation in children.
'If we are serious about controlling influenza infection in all ages, immunisation of our children is a must.'