Highways issues are invariably very complicated. Problems of ownership, the extent of the highway, duties of the Highway Authority, duty of adjacent land owners, and of course those of us who own some highway, adopted/unadopted, footpaths, bridleways, BOATS and so on. Every problem/incidence has to be looked at on its merits, and on a forum such as this it is nigh on impossible to reach a definitive position as you can't see the site, its surroundings which would help you to understand the wider context. You only have very limited information on the problem. This is my disclaimer because I can see some of what is coming. I'll try and answer those questions in due course.
ukmicky wrote:where does it state in the highways act or your quote that the work can be carried out without 14 days notice whether they wish to recover any cost or not.
Highways Act 1980 can be found here http://www.legislation.gov.uk/ukpga/1980/66/contents
s130(3) and s130(5) are the bits I think you are looking for.
ukmicky wrote:By doing it without notice it will prevent the owner of the hedge utilising their right under the highways act of challenging the the highways in their wish for it to be cut back at a magistrates court
The hedge owner also has a duty not to obstruct the highway. You seem to be suggesting otherwise, that is, it is acceptable to stop up or obstruct a highway unless challenged, at which point you can appeal. The old adage once a highway, always a highway remains true, you cannot stop it up or obstruct, well not without jumping through the proper hoops. Also of interest at this point, and depending on ownership, always a thorny issue, Lemmon v Webb would still apply. I.e. if the Highway Authority were the owners of the land over which the highway passed they have the right to cut to the boundary and as high as they like without notice.
As has been said previously the Highways Authority should only do what is necessary, and this is especially true if they do not own the land, as to how much that is, that would be a matter for the Courts to decide on the evidence before them should a case arise.