At Ashley Down Infants' School in Bristol, 22 out of 72 parents are so far refusing to allow their children to sit the tests, originally known as SATs.
Headteacher Patricia Chubb, who initiated a public statement against the tests signed by more than 1,000 fellow heads, said the campaign was now up to parents, following the National Union of Teachers' ballot to end the boycott and the Government's decision to close legal loopholes.
This year Jenni Pizer, a mother of four and former nurse, is leading the Ashley Down parents' rebellion with the support of the teachers. The governors, though sympathetic, have not committed themselves to a boycott.
She said the parents were against the external tests because they were "completely unnecessary, unfair and educationally unsound" and because they had cost "more than Pounds 500 million over four years".
Lorna Davies, of the parent-led National Campaign Against SATs, said: "I think there will be an upsurge in parental withdrawal of pupils, but it is early days yet."
In other counties, however, evidence of rebellion is thin on the ground. In Kent and Birmingham, education authority assessment officers said it was too early to say how the tests would go.
Just over half of schools with seven-year-olds submitted results for national analysis last year, Department for Education figures revealed in January.
The National Anti-SATs Campaign, which is dominated by members of the National Union of Teachers, is drawing up a register of schools which want to continue the boycott against the national tests.
It fears this year's test results for seven-year-olds will be leaked to the media and turned into "league tables". Campaigners are also suspicious of the conferences run by the School Curriculum and Assessment Authority this summer to review assessment. NASC fears that teachers' concerns will be sidelined by the SCAA agenda, and intends to raise the issue at the NUT conference in Blackpool.
If the conferences turn out to be what they consider a charade, NASC members will discuss seeking a ballot on boycotting the tests.
SCAA said in January that its review of the school tests for seven, 11 and 14-year-olds would be "full and thorough".