My experience is that not many trees in this part of London have TPOs on
them, or indeed in much of London. They are not automatically subject to
them in Conservation Areas, and indeed have to meet certain guidelines
before they would even be considered. However, if it has one don't touch it
until you have obtained full permission.

If you wish to prune or remove a tree, or any plant with a girth of more
than 7 centimetres at waist height, you are still required to give notice to
the Council before you undertake any work, and they are at liberty - under
certain quite restrictive conditions - to refuse. Seven centimetres is
rather small and there is no distinction between a bush, shrub, tree, etc.
Be aware of this because nosey neighbours love to fuss about trees. If you
make tree officers nervous they may slap a TPO on the tree in order to avoid
the possibility of gung-ho action.

As far as friends in high places goes, that is not my experience. It is my
experience however that tree surgeons and garden contractors are more likely
to get what they want as they are independent of the property and have a
reputation to consider. As a contractor I wouild be bl***y stupid to wreck a
tree for a few hundred quid and get the Council on my back for ever and a
day, and a fine, and the awkardness of having to face the same rightfully
suspicious and indignant officers next time I wanted to work in that
borough. As such we tend to try to do things properly.

As far as costs are concerned, tree surgeons are expensive because they
carry risks and specialist insurance. If the tree is big they are your best
bet, if it is under 20-30ft then a garden contractor might be cheaper.

Hope this helps

James