Tens of thousands of schoolchildren missed their Sats tests today because of a boycott by headteachers, as union leaders warned they could not rule out further action.
Across England, primary heads refused to administer the tests as part of industrial action staged by two teaching unions.
Christine Blower, general secretary of the National Union of Teachers (NUT), estimated that support ranged from 30% in some areas to more than 70% in others.
She added there were "categorically" enough schools taking part to scupper league tables - a key aim of the boycott.
Mick Brookes, general secretary of the National Association of Head Teachers (NAHT), raised the possibility of further action if the two unions - who confirmed the boycott last month - fail to reach agreement about the future of the tests with a new government.
He said: "We know that there are tens of thousands of children not sitting the tests today, that's what we hoped. It's been an opportunity for colleagues who want to see the system changed and improved to make a protest.
"The coverage of pupils doing the tests is quite patchy, but there appears to be patterns emerging.
"There have been areas where great numbers of colleagues are clustering together in support."
Mr Brookes added: "We would far prefer to negotiate than take action, but if pushed that's what we will do.
"We can't rule it out, but I do sincerely hope it doesn't come to that."
Ms Blower said: "Thousands of schools across England have decided that enough is enough and have taken the decisive step of boycotting this year's Sats.
"There are reports from many areas that a significant majority of primary school pupils will not be sitting Key Stage 2 tests this week. This will make the annual ritual of naming and shaming schools through league tables impossible."
She urged the new Government - of whatever colour - to begin "constructive talks" with the teaching profession about reforming tests in primary schools.
Echoing Mr Brookes, Ms Blower warned: "The campaign to end Sats will continue and I urge the next Government to pay immediate and serious attention to the matter of ensuring our schools have a fair and sensible alternative to Sats in place for next year."
Around 600,000 10 and 11-year-olds were due to take Sats this week - starting with reading tests today, followed by writing and spelling papers and then maths exams on Wednesday and Thursday.
As well as throwing league tables into chaos, the boycott could also affect Ofsted inspections as Sats results are a key measure used by the inspectorate when forming judgments on schools.
The two unions confirmed the boycott last month after ballots of their leadership members showed support.
It is down to heads, deputies and assistants to decided whether to take part in the boycott.
Angie Leonard, head of Lindale CE Primary School in Cumbria said she had a number of reasons for taking part.
"I don't think they (the tests) are the way forward in assessing children," she said.
"I think they can narrow the curriculum that's taught to primary years students."
Sats are also stressful for many children, parents and teachers, she added.
Ms Leonard said that six primary schools in her area were taking part, and plans had been made to ensure children are still assessed.
"We are organising ourselves and we are going to do some moderation between schools on our teacher assessment."
Mick Murphy, head of Rounds Green primary school in Sandwell, said his Year 6 pupils were taking past papers when teachers believe they are ready, which will feed into end of year assessments. The results will not be sent off.
A survey conducted by the Press Association over the past week found that an estimated 1,010 schools in 37 local authorities are boycotting the tests.
Among those with high numbers of schools boycotting the tests are Barnsley in South Yorkshire, where the council said more than half of its 78 primaries are taking part.
In Manchester, 60 schools confirmed they will be backing the action, as will all 31 schools in Hartlepool. In Hertfordshire up to 32 schools could be boycotting.
Some 21 local authorities said they do not yet have figures, with several saying schools have not been in touch with them. Five said they were aware of no primaries taking part in the boycott in their area.
The local authorities which said they expect the boycott to go ahead in some of its primaries are: Reading, East Sussex, Windsor & Maidenhead, Poole, Essex, Birmingham, Kent, Hampshire, Calderdale, Rotherham, Kirklees, Hounslow, Gloucestershire, West Berkshire, Lincolnshire, Darlington, Doncaster, Norfolk, Enfield, Middlesbrough, South Tyneside, Stoke on Trent, Southwark, Bromley, Portsmouth, Barnsley, Swindon, Hertfordshire, Peterborough, Lambeth, Manchester, Hartlepool, Westminster, Barking and Dagenham, Bexley, Kensington and Chelsea, Harrow.
The boycott was expected to be the first battle a new government would have to face, but with a hung Parliament following Thursday's General Election, it appears there has been no last ditch move by politicians to get it called off.
Both Labour and the Conservatives insisted that Sats should not be scrapped, although Labour said the system is "not set in stone". The Tories and the Lib Dems pledged to reform the tests.
The unions - which together represent around 80% of primary school heads - argue that the tests are bad for children, teachers and education, cause unnecessary stress and lead to the creation of league tables which undermine the work of schools and heads.
The unions have insisted that the boycott is industrial action with no downside, as children will still be attending schools and taking part in normal lessons.