You will need to ascertain where the damp is coming from e.g. ground behind the wall, rainwater penetration, overflow, burst pipe….
If it’s a “simple” building fault or defect in your own flat, the liability is yours. If it’s due to lack of guttering or somebody else’s burst pipe it could be a shared or somebody else’s liability. You won’t know for sure until the cause is established.
But firstly go back to your surveyor who should have picked this problem up for you at time of survey.