Yes, anyone, including a neighbour, can report suspected unauthorised development to the local authority, and the council can choose to investigate regardless of who raised the concern. The authority assesses the merits of the complaint independently rather than acting simply because a complaint was made.
There is no restriction on who can bring a suspected planning breach to a local authority's attention; neighbours frequently do so, particularly where they believe a development affects their property, such as an extension close to a boundary, overshadowing, or overlooking. The planning authority does not need permission from anyone to investigate, and a complaint from a neighbour is treated in the same way as one from any other member of the public.
Once notified, the council decides for itself whether the complaint raises a genuine planning issue worth investigating; it is not obliged to act simply because a complaint has been made, and disputes that are really about civil matters, such as noise, trees, or personal disagreements rather than unauthorised development, generally fall outside its enforcement remit. If the council does investigate and finds a genuine unauthorised development, it will proceed through its normal enforcement process regardless of the neighbour dispute that triggered it.
If you are concerned that a neighbour may report you, the safest approach is to check your own planning position, for example by confirming whether works fall within exempted development limits, whether existing permission was correctly implemented, and whether a Section 5 declaration might give you certainty. Being proactive is generally better than waiting to see whether enforcement follows a complaint.