Anyone who made a representation on a planning application, and/or presented evidence during an appeal can challenge the eventual decision. This challenge can only be on the basis of legal, rather than planning grounds however.
In other words, you cannot simply object on the grounds that the decision-maker should have reached a different conclusion.
If you are considering a legal challenge, you should discuss the case with a specialist planning lawyer.
This application must be made within six weeks of the date of the decision letter.
It is a highly technical proceeding and can result in significant legal costs, although these will be recovered if you win.
An application of this kind must be lodged within three months. In this case, you must be able to show that the local authority made an irrational decision or that there was some procedural irregularity.
You will need lawyers, but legal aid is available.
If you cannot find grounds for a challenge, don't give up.
The development will not necessarily go ahead, even with planning permission.
There may well have been changes in circumstances since the application was first submitted.
The developers may have decided to pursue interests elsewhere, or the development as first proposed may no longer make commercial sense.
The very fact there there has been a strong, well-argued campaign against it may persuade the developer to think again.
See CPRE's guide to challenging planning decisions in the courts, Plan B.