Other legislation concerning trees:

Most of the cases that result in legal action as a result of damage or harm caused by privately owned trees are dealt with under Civil Law and are decided based on legal precedent, judgements that courts made in previous cases, usually involving disputes between private individuals or between individuals and organisations. 
This contrasts with Criminal law which involves cases brought as a result of an alleged infringement of a statute passed as an  Act of Parliament. The Town & Country Planning (Tree Preservation)(England) Regulations 2012 form the basis of the legislation covering TPOs and trees in Conservation Areas which are dealt with HERE (TPOs) and HERE (Conservation Areas).
Other aspects of the law as it applies to trees are outlined below:

The owner of the land on which a tree is sited is ultimately the person responsible for its safety; she or he has a duty to take sufficient care to  avoid acts or omissions which it can reasonably be foreseen would be likely to cause harm.
'Reasonability' is key; while land owners should act where a danger is apparent, that should not amount to an unreasonable burden; it should not force the landowner to act as 'an insurer for nature'.'

Foreseeability' is also important. One cannot be held liable for issues arising from causes that were not 'reasonably' apparent.  
Yet what is apparent to one  'reasonable' person may be anything but apparent to another and this is especially true of trees.

For this reason it is advisable that trees in any location where their failure could result in harm should be regularly inspected.  In private gardens it may be sufficient for the property owners to monitor their trees themselves, calling for professional advice should anything is observed that might cause concern.  In more high-risk situations, such as trees near roads and other well-used locations, a regular program of tree inspection by a professional might be called for. The frequency and thoroughness of inspections will depend on a range of circumstances

 The National Tree Safety Group has published some valuable guidance in the form of a booklet ‘Common sense risk management of trees’ . The full text and a summary document are free to download HERE

The protection of birds, bats and other wildlife is largely contained in the Wildlife and Countryside Act (1981) (as amended) and in the Conservation of Habitats and Species Regulations (2017) (as amended). Amongst their provisions are the following:

• Anyone takes, damages or destroys the nest of any wild bird while that nest is in use or being built; or takes or destroys an egg of any wild bird  is guilty of an offence. There is a ‘close season’ for birds from 1st February to 31st August

  .
  More advice on Birds & the Law is available HERE
  

• All bats are protected under the Wildlife and Countryside Act (Schedule 5). They are

  also included in Schedule 2 of the Conservation (Natural Habitats, &c) Regulations

  1994, and The Countryside and Rights of Way Act 2001. The Acts and Regulations

  include provisions making it Illegal to ‘recklessly or deliberately kill, injure, capture or

  take bats; to recklessly or deliberately disturb bats (whether in a roost or not and to

  damage, destroy or obstruct access to bat roosts. (A bat roost is interpreted as 'any

  structure or place which is used for shelter or protection’, whether or not bats are

  present.

  
  The above will limit and may prohibit certain tree pruning or felling work during

  spring and summer. Bats will use roost sites in trees between April and September,

  depending on weather conditions. Some species may hibernate in large old trees,

  during the winter months.

  More advice on Bats & the Law is available
  More advice on Bats & the Law is available HERE

Under The Highways Act 1980 a tree owner is responsible for maintaining trees, hedges and shrubs within their own property that adjoin onto the public highway. You must make sure that the vegetation from your property does not overhang the pavement/road so as to obstruct pedestrians or vehicles.
The Act also imposes a duty on Highways Authorities to “prevent, as far as possible, the stopping up or obstruction” of a public highway. They may serve notice requiring the cutting or felling of a hedge, tree or shrub which “endangers, obstructs or interferes with the passage of vehicles or pedestrians, including the view of drivers or the light from a street lamp.” Such works are required to be carried out within 14 days of the notice being served.

The local authority can issue a Section 154 notice to compel a land owner to deal with a dangerous tree within falling distance of a highway. if the owner fails to do so they may invoke the Miscellaneous Provisions Act, which gives a Local Authority certain powers, including right to deal with privately owned trees that are regarded as representing an imminent risk to person or property; see below.

The Local Government Miscellaneous Provisions Acts of 1976 and 1982 confer a wide range of rights and duties on Local Authorities to deal with perceived dangers and nuisances affecting the public; Section 23 of the 1976 Act grants a Local Authority discretionary powers to deal with trees where there is an imminent risk fo them causing damage to persons or property. dangerous trees. 

This may arise when a tree owner is aware of a tree on their own land which represents an imminent danger of causing significant damage to persons or property, but which the tree owner is unable to undertake her or himself. However the Council may also take action when a dangerous tree is on third-party land but the owner is unwilling to take appropriate action, or else cannot be contacted within a suitable timeframe. If necessary, under section 24 of the Act, the Council has the authority to enter private land in order to ascertain the condition of the tree and to take the necessary action to make it safe.
These powers are discretionary and are intended to be used as a last resort or in emergency situations.

In such cases, the Council has powers to recoup the full costs of all work undertaken plus administrative costs.

Further information is available HERE

These Acts includes provision to impose a  duty which an occupier of premises owes ‘in respect of dangers due to the state of the premises or things done or omitted to be done on them’. From this it follows that they must take 'reasonable steps' to ensure that the trees on their land are in a safe condition and do not place people or property at risk.

The 1957 Act deals with liability relating to persons who enter land or premises either by invitation or by permission.
The 1984 act extends liability to other persons, including trespassers. In other words, occupiers can be held negligent in their duty of care even if injury or damage occurs on land where people do not have access by right or by invitation.

This requires that risks both to employees and third parties be reduced so far as is reasonably practicable.
It has been used by the Health & Safety Executive to prosecute a local authority following fatalities arising from the failure of a local authority tree that had been severely decayed for some time, the dangerous stae of which the authority had failed to recognise. 

There is no automatic right to light or a view in English law.
The Rights of Light Act 1959 states that if a property has received daylight for the last 20 years, the occupants may be entitled to continue to receive that light. Thus if your neighbour erects a structure that restricts the daylight to your property by blocking daylight reaching a window, there may be some legal redress. In theory the same case can be made for large trees blocking light. However, such cases rarely succeed, largely because trees grow slowly and it is difficult to be precise about when the loss of light occurred.