Ok. You should get a survey and this would deal with the actual or risk of damage. That is helpful because then if it goes to Court, you can rely on it.
Once you have the report you can share it with your neighbour and this will deal about what can be done.
But as for the trees anyway, anything which overhangs then you are entitled to cut back to the boundary line.
if the neighbour refuses to carry out the work then you can seek a Court order.
You would need to complete form N208:
Also form N16a:
The Court will list the matter for hearing and you can use the report. The Judge will decide whether to make an order requiring the neighbour to carry out the work.
If the Court does and the neighbour refuses this is contempt of Court which he could be warned, fined or sent to prison
Can I clarify anything for you about this today please?