Wind farm operators E.On Climate Change Renewables and RES UK and Ireland were refused planning permission by King's Lynn and West Norfolk Borough Council in 2011.
They later went on to appeal the decision and in May, the planning inspector allowed the two appeals and granted permission for the wind farms, despite opposition from residents and conservation bodies including English Heritage.
Now the two action groups - Against Turbines At Chiplow (ATAC) and Creakes Action for Protecting the Environment (CAPE) – are seeking a ruling forcing the communities secretary to have the two applications reconsidered.
The two groups, which claim to represent a large number of local residents, claim that they will be visible from Bloodgate Hill Fort, a protected ancient monument of national importance.
Government adviser English Heritage told the inspector that the wind farms would "diminish the public experience, perception and understanding" of the Iron Age fort, in particular the Jack's Lane wind farm.
In their legal challenge, the two groups claim that the inspector failed to take into account a key expert's oral testimony that the harm would be greater than he first indicated in his written evidence.
They say that a Dr Edis, an expert put forward by E.On, initially said that the Chiplow scheme would only have a "minor" adverse effect on the fort, but, in his oral evidence, revised that assessment upwards to "moderate" and "noticeable".
They claim that he also stated that, as a matter of calibration, his assessment of the harm that would be caused by the Jack's Lane scheme - which he had classed as "moderate" - would also have to be revised upwards.
However, they say that the inspector failed to record or remember Dr Edis' oral testimony, and reached the conclusion, based on his written evidence, that the harm caused by the two schemes would be "minor" and "moderate" respectively.
They say that this mistake was material to the inspector's decision and that, had the harm from the Jack's Lane site been upgraded to "substantial", he would have been required to refuse permission unless there were substantial public benefits.
They argue that, even if the proper conclusion was that its significance was "not quite major", the mistake could have caused the inspector's decision to be different when the cumulative impact of the two wind farms was weighed in the balance.
As a result, they say that the inspector failed to take a material consideration into account, failed to provide adequate reasons and reached a decision that is not sustainable.
The judge is expected to reserve her decision in order to give it in writing, likely in the New Year.