Hi Micky and welcome!
How many postcodes do you have in your country? This could be a long query. You probably don't want to pull all of these down into a dropdown since it will be too hard to search the list. My suggestion would be to have them enter a value and then query the second table (Local District Office E-mail addresses) and display that. That means the user will have to know the postcode, but that is probably a safe assumption.
To do this, unfortunately, in InfoPath there is no way to pass a parameter to a SQL query. You will either a) have to write some code, or b) use a Web service. We have a Web service that allows you to filter SQL queries based on values without requiring code.
Send me e-mail, if you'd like to try our Web service.
Regards,
Patrick Halstead
Project Manager at Qdabra