The Party Wall etc Act is seperate from Planning and Building Control. The LA will (in all likleyhood) not take any action on Party Wall matters. The Act has no provision for compensation or redress. Additionally, you have no right to stop your neighbours work.
However, you have a right to see the work completed to a satisfactory standard (if the Act applies).
Just because they are building adjacent your propoerty does not automatically trigger the Act. There is very specifc critera in regard to work to the wall, and adjacent excavations. To see if the Act applies, consult a Party Wall Surveyor available through the RICS; or alternativly, search for 'Party Wall Pyramus and Thisbe' to throw up information.
I suggest talking to your neighbour reasonably. Try and make this work.
An injunction will halt his work, but they cost a fortune, and if sucessful, only mean your nieghbour must follow the process. Works will proceed pretty much unaltered (provided their design is sound). Additionally, Party Wall injunctions have a nasty habit of costing the Adjoining Owner (you in this case) an awful lot through claims for delay. Don't take out an injuction in the hope it will sort things out, and if you are considering it, find a solicitor from the Technology Courts familiar with the Act.
As an aside, forget about tresspass unless there is significant transgression or damage; it is a nightmare.
What I would suggest you do is contact Building Control and Planning to seek copies of your neighbours consents (do this is writting, but also check online).