As a 'bottom line' draw the seller's attention to the fact that you are unhappy to proceed unless they agree to reduce the price by the amount you are quoted to fix the problem (plus inconvenience).
They may deny any problem except on account of possible poor air circulation alone.
They may say that it is only minor and would be covered by a 'service charge agreement' but that is not good enough, especially in the case of major problems, as residents can be extremely 'difficult' when it comes to forking out for someone elses issues and it could be difficult and time-consuming to enforce this by taking legal action anyway.
Some damp can be caused by drains leaking, owing to growth of tree roots, or minor subsidence, also a high water table.
Slope drainage can be another causes especially in those Victorian properties built to drain at a different level at the rear which becomes an issue for a variety of reasons.
The house insurance should cover such issues but can take months for the insurer to take measurements and agree to costs of remedial work, cutting roots back and putting cement walls or piles into the ground.
In the current weather conditions, subjecting the ground to seasonal drought and then to wet ground the earth expands and shrinks causing cracking in buildings and damage to drains.
You really need to to take a view on the likely severity of the problem but it happens in many properties and nothing to do with the sea either, unless it washes in !!

Does it look damp around the outside of the property and especially at the rear.
I know what damp means in a kitchen area - slugs crawling around at night, but if that is all and it is only minor damp I may be blowing this out of all proportion.
Good Luck !!
