Well Lucyeve.
This is not an unusual or unsurmountable situation and you should not be getting so upset on this aspect of the failure to sell your house. Selling is a bit difficult at the moment, you will sell it just takes a little longer. Your so called 'Estate Agent' to say the least 'would not fill me with confidence' and you should consider changing. The 3 buyers who were introduced should have been checked out to see if they had loan approval before they were introduced to you. Now the agent is getting worried and maybe anxious about not getting any fees, Is it possible that he is attempting to devalue your house so that you may be more willing to reduce the price of your house below that which is reasonable at this time and thereby make it easier for him to sell.
Unless this extension is like the house that 'Jack' built then he does not know what he talking about,the mention of 'dampness' is meant to put the fear of God into us. I can see no reason for this unless for some reason it is causing dampness to your house at the moment. It should not be a problem to any new work.
1. You say this ext 'is built up from the party wall',does this mean that you can still see the old party wall and his wall is ontop of it, or would you know if the old wall was removed, in which event the wall was possibly built on the party line.
2. Are any parts of the adjoining extension, gutter, facia and soffit, or pipes oversailing your property or is it a straight wall with a capping on top which would be the best situation.
3. Do you know how long this ext, is built, not that it makes much difference but it could be a factor.