There seem to be a few loose ends in this thread. In the interest of leaving the thread a bit tidier as a reference resource, I am going to have a shot at summarising. I suspect I will regret it.
There are three parties as I see it. The tree owner, the development site owner (whether he is the developer or the person selling the land) and the public sector (generally the Council).
Firstly for trees that are not protected by TPOs or CA status at the time development is proposed.
The tree owner has to tolerate the removal of roots in the site and overhanging branches, as long as this is not done mischeviously. He could ask the Council to intervene and TO the tree.
The site owner can remove roots in the site, just as he can overhanging branches. This can be done with or without development proposals.
The Council can make a TPO to prevent unconsented work to the tree, if it considers it expedient to do so for the amenity of the area. They can alternatively or additionally put forward conditions in a planning consent that protect part of the tree and its roots that are on the site, even if the stem of the tree is on other land.
Secondly for trees that are TPO'd already.
The tree owner cannot do anything to the tree or its roots without TPO consent, unless the planning consent for the site allows such work.
The developer cannot do anything to the tree or its roots or branches, even the parts in or over the site, without TPO consent. The exception is that if the planning permission explicitly or implicitly recognises that the tree works are needed to implement the consent. In that case a separate TPO consent is not needed. Any work beyond that which is necessary to implement the consent is unlawful. If the site owner does not have the tree owner's permission to do work to the tree he can only do what he could do at common law (see first scenario).
The Council can make a TPO when it learns of the development proposals if it has reason to believe that the tree should be protected for its amenity contribution to the area and is under threat. This would protect all parts of the tree against wilful damage or destruction. The roots would thus be protected. It can also impose conditions on any work that might affect the parts of the tree that are in the site. The 'site' is the application site. It is not generally competent for the Council to impose conditions on any land that does not form part of the application site, whether the development site and the application site have the same boundaries or not.
I think that's the gist of it as I see it. Please anyone correct me if I'm wrong.
Anyone acting on this advice does so at their own risk. Please verify it independently before acting. I cannot be held responsible for trying to be helpful for free.