Three people were arrested from the property in Lowergate on suspicion of firearms offences as part of a pre-planned police operation last night.
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No firearms were discharged and searches are still ongoing.
A further arrest was made at an address on Bradshaw Street in Nelson this morning.
The address on Lowergate is opposite St Michael and St John's RC Church and the adjacent St Michael and St John's RC Primary School.
Parents and children on their way to school this morning had to walk past the scene of the incident which has been taped off and is still being guarded by police officers.
Assistant Chief Constable Terry Woods reassured local residents that, despite the continued presence of police officers, there is no ongoing threat to the local community.
The incident is in no way connected to Keystreet music bar, which is situated on the opposite side of the road.