Central Bedfordshire Council, a unitary authority, states the conservation area rule as "If you would like to carry out works to a tree in a conservation area, you will need to give us at least 6 weeks notice", with the notice given through the Planning Portal, and says it will enter the proposal in the Register of Proposed Work to Trees in a Conservation Area. On what is covered it states that "Any tree with a stem diameter over 7.5cm (measured at a height of 1.5m) is protected in a Conservation Area regardless of species, age, or visibility". Dunstable has its own conservation area.
On orders the council states that an order acts to protect the tree from damage, that where a tree is subject to one "you must apply for permission to do any works to the tree", that carrying out works to a protected tree without permission is illegal and can carry a fine of up to 20,000 pounds. gov.uk guidance distinguishes destructive offences from other contraventions and explains that penalties can include an unlimited fine, and the amount that applies turns on the offence and the court. The council also says that any planning application involving work to or near a protected tree should be accompanied by a Tree Report.
The national control behind that notice is the section 211 notice. gov.uk describes it as a requirement to notify the local planning authority "6 weeks before carrying out certain work on such trees, unless an exception applies", and says consent from the authority lets the work go ahead sooner. It also states that consent "is needed for carrying out work on diseased and/or dying trees unless some other exemption applies".
The Forestry Commission service sets the felling side. A licence is needed to fell growing trees in England unless an exemption applies, with the threshold at an over bark diameter of 8cm or more measured at 1.3m above ground level, or 15cm or more for coppice or underwood. Subject to the applicable exemptions a licence is required above five cubic metres per calendar quarter, and the five cubic metre exemption allows no more than two cubic metres to be sold. Licences are free in England, and trees in private gardens are among the listed exceptions.
Wildlife law runs alongside the tree controls. The gov.uk wild birds page states that taking, damaging or destroying a nest "while it's being used or built" is against the law, and the gov.uk bats page states that every bat species, its breeding sites and its resting places are fully protected. We would set both out on the rules page and link them.
We would explain how you check the conservation area boundary, any tree preservation order and the proposed work before confirming whether a section 211 notice or consent is needed.