I saw plenty of retired officers pitch up in uniform to ACM Moran's memorial service, which was attended by the Duke of Edinburgh as well as all the VSOs; nobody worried about it. If you want to wear your uniform (usual caveats re appearance) to a Service funeral, crack on.
For Heathrow Director, use of rank technically depends on how your retirement was Gazetted - assuming you were not going under some sort of cloud, the phrase was normally "retaining the rank of ...". So, yes, you are perfectly entitled to use the rank, but it is a matter of personal choice (and circumstance) whether you do so or not. For example, someone attending a Mess function as a guest might well use their rank, whereas when working in your second career making widgets in Company XYZ, most would opt to stay as Mr.