Finding matches where GROUP BY COUNT(*) is 1
This query should help you out.

It works with an delivered table named org_type what filters out double org_id.

That delivered table will be matched with where filter org_type.type_id = 2 to make sure that type_id = 2

SELECT 
   org_type.type_id
 , org_type.org_id
 , organisation.name
FROM (
 SELECT 
     type_id
   , org_id
 FROM 
   org_type
 GROUP BY
   org_id
 HAVING 
   COUNT(*) = 1
) AS 
  org_type
INNER JOIN 
  organisation
ON
  org_type.org_id = organisation.id
WHERE 
  org_type.type_id = 2