Permission was sought for a period of 30 months to provide classroom accommodation for use while a new assembly hall, classroom block and ancillary building is built.
The temporary accommodation will be removed as soon as the permanent facilities are completed.
The Environment Agency had no objection.
Herefordshire Council's Traffic Manager raised no objection to the application but encouraged further discussion regarding the travel plan and parking arrangements for the school to reduce the impact of traffic in the vicinity.
Much Dewchurch Parish Council expressed concerns, saying the site is outside of the settlement boundary and the buildings would be visible from the church and churchyard.
Thirty four letters of objection were received, concerned over the existing temporary buildings on the site, car parking provision and that the plans would detract from the setting of the village and grade I church.
Six letters of support were received, saying it seemed sensible to allow temporary buildings as this would allow the school to function during the building works.