The north Shropshire branch of the far-right party said the decision made by Shropshire Council planning officers should have been made at a full public meeting rather than in private.
And they have written to Shirehall in protest over how the issue has been handled.
Phil Reddall, organiser of North Shropshire BNP, said he had made a complaint to Shropshire Council due to the decision being delegated to the planning department.
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The 19th century building in Oswald Road, will provide a permanent home to Oswestry Muslim Society for the first time in its 10-year history. George Miah, chief adviser of the society, has previously said the organisation hopes to build bridges and gain better understanding in the community through the facility.
The £300,000 project will see the building, currently a furniture store, converted back into a place for meeting and worship. Work will include internal alterations and the creation of a one-bedroom, residential unit.
Mr Reddall said: "Maladministration has been cited as I believe, given the comments received from the public and the culturally significant nature of the application, the council had a moral duty to make a decision as an elected body, thus being fully accountable to the electorate."
The letter Mr Reddall has sent to the council, says: "I believe the council have acted with maladministration regarding their decision to allow planning officers to deal with this case rather than deal with the application as a council at a public meeting.
"I understand that in passing this case to the planning department, the council have acted in accordance with their own regulations, however I believe that they have acted without due consideration.
"Given the application received 103 public comments with the majority being objections, I insist the council should have made an electorally accountable decision."
Mr Reddall said he was awaiting a council reply before deciding his next move.