Mr Evans said: "Children do gain enormous benefit from the extra revenue that parents' groups raise but it's not the child's fault if, for whatever reason, his or her school's support group cannot raise extra money.
"How can we try to ensure those children who attend schools in less prosperous areas are not the same children who have fewer library books, older or weaker computers and generally less equipment?
"I suggest directing money from the lottery to those schools that do not benefit as much from revenue from their parental support group's fundraising. "
According to a National Confederation of Parent-Teacher Associations's survey, parents contribute Pounds 1.2 billion to school funds.
Mr Evans, MEP for London North West and Labour's European education spokesman, hopes that such ideas will be listened to, and acted upon, now there is a Labour Government.
He believes the SEA should be modernised and reorganised to fit the new structures of the Labour party and Government. Part of this repackaging could include changing the SEA's name to the Labour Education Society, thus removing the dreaded S-word from the title.
The SEA has an impressive membership list. Stephen Byers, minister for schools standards, is its vice-chair and 19 other ministers, including Chancellor Gordon Brown, President of the Board of Trade Margaret Beckett, Education Secretary David Blunkett, and many MPs, are all cardholders.
But in recent years it has not increased its 1,500 total membership and has now been overtaken by the Christian Socialist Movement which has 5,000 members.
There has also been internal dissent over its direction. One member said: "The SEA has got to increase its membership and has got to be involved in implementing as well as trying to influence policy.
"It has been involved too long in fighting Tory education policies, and now it should reinvent itself and put forward positive documentation of good practice. It needs to send out the right signals to the Government - that it is forward thinking and innovation."
There are signs that changes are on the way. There is a renewed interest in elections to its national executive, with candidates including Neil Fletcher, former leader of the Inner London Education Authority, Val Shawcross, leader of Croydon Council, and Tony McNulty MP.
The contest for chair between Robert Evans and the incumbent Max Morris could be seen as a battle of old Labour versus new, and not just because Mr Morris is in his eighties and Mr Evans is 40.
Mr Morris is a former member of the Communist party and a former president of the National Union of Teachers. In the past he has described himself as left but not ultra-left.
In his election address, he says: "We must remain Labour's educational conscience."
He says the SEA must support the future of comprehensive education, which he describes as its "contribution to labour ideology" and the raising of standards.
Mr Evans believes the SEA (should become a think-tank run by the grass roots.
He said: "The SEA has to be aware of its image. It contains a large number of MP members, including members of the Cabinet. This is a powerful force and we have to be able to make that power count in our favour.
"The role of the SEA must be supportive, but not uncritical, of Government. We should use the great expertise at our disposal at all levels from the classroom practitioner up to those that inform policy."
The result of the vote for chair will be decided on Sunday and the SEA will have an opportunity to discuss a name change at its annual conference in Bristol next Friday.