Urgent advice required regarding compromising of nesting birds

Hello Today my neighbours had a lot of the tree outside their property chopped including lots of the top branches where there are nesting wood pigeons. I did not realise how much of the tree they would chop down and now the nest has been left at the top, exposed to the elements with a poor pigeon sitting on top. Earlier this evening there were several magpies showing interest in the nest and in the tree itself. Is there anything that can be done to help this situation? I hadn't realised that it was illegal to chop a tree while there are birds nesting in it. Unfortunately I did not get the number of the 'tree surgeons' although the name on their truck said Ayres and Sons, Tree surgeons. Please can you let me know how I can help?