Ok firstly, go back to the people who carried out the survey, let them know you have an issue and why was it not identified. Even if you bought the cheapest service (Condition Report) a damp meter should have been used.
Secondly, the damp on the chimney can be several things or all of them. Loose flashing or cracks in stack, as noted above.
However, it could also easily be the fact that the building has been left cold and unvented with no cowl on the chimney. This will let rainwater down the flue without any ventilation or heat to keep it dry.
It could also be a salt damp issue, where burning fossil fuels produce salts that collect on the plaster surface and attract moisture.
None of these should be too expensive to fix but get it checked out.
As for the cracks, you will always like get small cracks in any building. It's only when they get larger, or progressive do they become and issue. That's not to say that it can't be structural movement, that can happen on a 1930's property as any, but usually if there's trees nearby or a drain issue. Again, get it checked by a Chartered Surveyor.