The FSA board yesterday declined to decide on what strategy to take, instead refering the matter to the executive for further consideration of the technical details involved.
The FSA also passed on the decision to the Department of Health.
In May the board decided to recommend that government make the addition of folic acid mandatory but did not make a conclusion on whether it should be added directly to flour or to bread.
The additive is seen as a means of increasing folate intake in women so as to reduce birth defects in babies.
An FSA report published earlier has recommended that folic acid be added at the milling stage to most flour, concluding that this strategy would have the least cost effect on industry as a whole.
However, concerns have been raised by various industry groups.
Chris Dabner from the National Association of Master Bakers told Bakeryandsnacks.com that the real issue would be the one-off cost involved in re-labelling.
"Flour is present in thousands of products often at extremely low levels," he said.
"If the flour is present at an extremely low level as a minority ingredient, then the amount of folic acid that it will contain will be absolutely insignificant and therefore to label its presence could be misleading."
He said that the FSA board either did not agree with this view or failed to take it into account when coming to their decision on folic acid addtives as a whole.
The comments follow concerns brought up by the Biscuit, Cake, Chocolate and Confectionary Alliance (BCCCA), whose members may have to consider importing folic acid-free flour if the additive is put in at the milling stage.
Dabner added: "In many respects we are no nearer to having an answer, as the question of what flours to fortify has now been referred back to the executive and FSA officials.
Manufacturers just want the FSA to make up their minds."
Gordon Polson, director of the Federation of Bakers, recognised the FSA failed to reach a decision yesterday over whether to fortify bread or flour.
"The Federation of Bakers looks forward to discussing with FSA how they can implement the decision, but we believe strongly that the only practical solution is to fortify at the milling stage - not in the bakery," he said.
The Soil Association recently opposed the FSA's recommendation and appealed for organic white and brown flours to be exempt from the recommendation, despite already being fortified with iron, calcium, niacin and thiamine.
Gundula Azeez from the organisation told BakeryandSnacks.com: "We cannot support food policies that accept the routine removal and degradation of nutrients by refining and other processing as normal, and then encourage the replacement of a few of the missing elements by 'fortification' with synthetic versions."
One of his concerns was the possible long-term effects of folic acid supplementation, an issue the FSA said could be addressed by appropriate labelling.
Andrew Whitely, the chair of the Soil Association processing standards committee supports Azzez.
"My main objection is that it is a crude form of mass medication which uses a laudable aim but a flawed method," he said.
He called this mandatory fortification an "admission of defeat" in that there is no other way of getting women to consume necessary amounts of folate than "sneaking it in to all the flour they eat" .
However, Polson added: "UK bakers are not for or against fortification, we believe it is a medical decision, however the implementation has to be carried out in a way which is practical, and hence it should be at the milling stage."
The UK exports £301m worth of biscuit and cake products per year and £56m of bread.
An FSA report has noted that the UK's trading partners would be less likely to import its flour and flour-based products once these are fortified with folic acid.