Your first sentence is entirely correct. Therefore I assume that when you say
you mean shooting inside Buckingham Palace. However the need for permission has nothing to do with copyright law and so it is confusing to then go on to talk about a licence to shoot in this way.if I want to shoot Buckingham Palace I need to get permission
I assume that what you are asking is: if someone has obtained permission to make a video on private property, does that allow you to use part of their video in your own work? There are two parts to this. First it will depend on whether the property owner has laid down conditions to the original permission which would prohibit this, or whether for instance the video was made, with permission, to record a private family event, such that section 85 of the Copyright Designs and Patents Act would apply.
And secondly it will also depend on whether you have permission from the videographer to copy part of his/her work, since I cannot see the fair dealing exceptions applying in most cases.
If the video maker has not obtained permission but publishes their video anyway, that will not invaildate any copyright in it and so you would still need permission to copy part of it. However in such circumstances, if the property owner objected (say, because the video covered private family matters) they might have a claim against you, as well as the videomaker, for breach of privacy contrary to Article 8 of the European Convention on Human Rights, by making the video available to the public.