Gillian Thorpe, key stage 1 and science co-ordinator at Sir William Burrough primary in east London, welcomed the announcement, saying that the curriculum needed to be slimmed down. "There is a lot of pressure on teachers and children - I just don't think there's enough time in the day to fit it all in."
Although she believed a stronger emphasis on numeracy and literacy was needed, Ms Thorpe did not want schools to teach only reading, writing and arithmetic.
"If children are going to have their imagination fired, they have to know why they are learning all these skills and know that they are able to use them in other aspects of learning," she said.
The school already devotes an hour each day to literacy and numeracy skills.
Mark Bennett, the school's deputy head and key stage 2 co-ordinator, said the curriculum was overcrowded and some subjects studied in too much depth, but he did not want those such as art to disappear.
He said the school might take the opportunity to spend more time on developing language skills. "We have a high proportion of bilingual pupils who need a lot of work on speaking, listening, basic grammar and colloquialisms."
With a steel band and a choir, music was one area the school did not want to neglect. Neither, he said, would it want to marginalise other areas of strength such as geography and history.
Mr Bennett did not want to see primaries, particularly those in inner-city areas, focus too narrowly on literacy and numeracy: "A broad curriculum enriches the children's learning and gives them windows of opportunity."
Any curriculum reform should be guided by consultation with the teaching profession, he said. "At the end of the day it's us who are delivering and managing it."
Betty Cowell, a Year 5 teacher at West Kidlington primary in Oxfordshire, said that her school recognised the importance of all types of literacy skills, but she feared that spending extra time on the four core subjects would be at the expense of more creative pursuits.
She opposed any narrowing of the curriculum and said schools should not forget about support that might be available from the local community. "Some children in all schools really need the creative aspects, because they're not very good at literacy skills."
Ms Cowell said Mr Blunkett's announcement was yet another example of teachers being dictated to. "In no other profession would you get people being told how to do their job. More and more, teachers are not being seen as professionals."
Martin Hall, a teacher at Westdene primary in Brighton, said his school had already begun to spend more time on literacy and numeracy.
From this month an hour will be devoted to English and an hour to mathematics each day, and 2.5 hours a week to science, leaving just 10 hours a week for other subjects. The total was reduced to only seven hours after PE and collective worship.
Mr Hall feared that there would not be enough time left to properly cover some non-core subjects, which will be taught as 14-hour modules.
"Teaching literacy and numeracy is very important, but so are other things. If we stuck to them and skimmed over the rest, we would end up with a generation of boring people." He too feared that pupils in inner-city areas could lose out even more than those who lived in more affluent areas.