Thank you for your question. My name is ***** ***** I will try to help with this.
You need to get a surveyor to look at the problem and to confirm exactly what is causing the damp. If it is the building of the conservatory across the so-called way then you have a claim against the neighbour in negligence.
Your claim is for whatever damages caused and for an injunction to make him put the job right.
If you have house insurance, you may have legal expenses cover that would pay for the cost of the litigation so it is worthwhile checking.
A solicitors letter threatening an application to court may provide the required result without the need to issue legal proceedings. It is not uncommon for neighbours, in situations like this, to simply ignore things if their property is not the one affected.
Can I clarify anything for you?