Many support the National Association of Head Teachers' call for governing bodies to resist the Education Secretary's plans by withholding key stage 2 results from the league tables.
But the union's call seems unlikely to be heeded by school governors who have taken note of Mrs Shephard's warning that such action would be illegal.
According to NAHT Norfolk branch secretary Michael Garratt, the Education Secretary's U-turn was "another example of people making facile judgments on weak evidence, causing huge problems". He predicted the call for a boycott would be "very sympathetically received by heads and probably by governors as well".
At a branch meeting on Monday, heads were "very disappointed about the lack of warning that results were going to be published". Mr Garratt added: "We were very unhappy with last year's key stage 2 tests. Parents and governors felt it was a shambles. Obviously, this year we hope they will be better but we have seen only two out of six exams."
Chris Young, head of a primary school in rural Stoke Ferry, voiced his objections with a suitably agricultural metaphor: "What would farmers say if you ranked their production in league tables? They would say 'This is not fair - my land is not as productive as his'. The same applies to schools. I don't think people who read the tables in newspapers have sufficient background to interpret them fairly."
He intended to share his misgivings with governors but admitted that "they will probably feel the results should be published".
Terry Plummer, head of Redcastle Furze first and middle school in Thetford, was also worried that league tables would lead to unfair comparisons. "Schools will vary in the way they approach the tests, in terms of training children and preparing for the tests," he argued.
The boycott was "certainly something I shall raise with my governing body, and something I can identify with," he said.
Chairman of governors, Alistair McGregor, was equally critical, but added: "There is a law that the information must be sent in. As governors, we want to set an example as well as guide the school and I would be reluctant to break the law. In the long-term we should be seeking to change the law, instead of this one-off gesture."
Dominic Cragoe, head of Abbey Farm middle school in Thetford, felt league tables were "unhelpful" but admitted: "If the law says something, I think we have to follow it whether we like it or not. I will certainly discuss it with my governors but I cannot recommend they withhold the results."
Jasmine Golson, head of a 45-pupil village primary, near Downham Market, accused Mrs Shephard of reneging on her promise not to publish exam results until the process was bedded down. "I am very cross about it. I shall be discussing [the boycott] with my governors next week and I shall probably back it although it has got to be the governors' decision," she said.
Margaret Pearson, head of Denver county primary, near Downham Market, warned: "We are going to have to teach children how to pass these tests, and get up the league tables - that is the game the Government wants us to play, but it is not going to be to the children's benefit." Her governors would want to make the results public, she predicted. "We are in the happy position of not having terrible results, which is a terrible thing to be saying."
Roger Yaxley, head of Attleborough junior school, was also concerned. "I only hope parents and the general public take this as one indication of the work of individual schools but realise there is a much wider picture." He sympathised with the NAHT campaign: "I will take it to my governors."
Clackclose primary in Downham Market, which has a learning support unit, is the kind of school which could be presented in an unfair light by league tables.
Head Stephen Capper had "grave reservations about their validity and usefulness. I feel it was a very clear commitment by the Secretary of State that the tests would have time to bed down".
The chair of governors, Sheila Nunn, a Tory voter and town councillor, refused to rule out a boycott.
"I know Gillian Shephard and I think she is a pretty good MP," she said, before going on: "Governors would not willingly wish to flout the law, but if our staff can convince us that withholding exam results would be in the best interests of the children at this moment, then I imagine we will support them."
Key stage 2 timetable
This week: the key stage 2 tests in English, maths and science for 11-year-olds took place
Next week: schools give test papers to the nominated external marker, employed by a marking agency under contract to the Government. In practice this will be one of five exam boards in England and Wales.
June 28: the markers send scripts and results to schools. Heads fill in large mark sheets with the results of their own teacher assessment. This is a point of confusion: the NAHT believes schools must do detailed calculations before returning the mark sheets. The SCAA says the exercise is no more than form filling.
July 31: schools return the completed mark sheets to the exam boards, who then analyse the information and pass it to the DFEE.
March 1997: the DFEE finally publishes the results for 14,000 primary schools, with or without the teacher assessments.