It does sound like a breach of the condition. They could submit a S73 to remove that condition. This would create a new planning permission without the condition. The original one would remain.
However, it is possible to give permission for the new dwelling if the local authority had not checked previous planning correctly.
If this is a current application, anyone objecting might wish to alert the planning officer via email of the issue.
As to reasons for objecting online, one would detail all the issues affecting neighbours.
Examples of VALID Planning Grounds
Contrary to Development Plan (Structure Plan or Local Plan)
Appearance (design, materials etc)
Traffic, parking or access problems
Residential amenity (noise, overshadowing, overlooking)
Drainage problems
Effect on setting of Listed Building or character of Conservation Area
Examples of INVALID Planning Grounds
Devaluation of property
Loss of view
Possibility of future problems (eg use of property)
Hours of Work and damage during construction
Business issues relating to the applicant
Possible fire hazard
Contended legal rights e.g. ownership
Errors of notification