When considering a planning application for proposed works, the Local Planning Authority will take into account (among other issues) any impact on light available to nearby properties. The LPA will assess the impact of the proposed works and its potential to harm to neighbouring amenity, and will make its decision in accordance with its assessment. It will not be bound to issue a refusal because of some legal constraint which is not within the planning laws and guidance; the grant of a permission will not remove other legal constraints, and if there was some legal right to light the proposed construction could still be challenged by the aggrieved party. This is not the situation as set out in the OP.
The information links posted above are a good place to go, other than legal advice from someone experienced in light and property law.