Lookup With Repeating Values

I have a spreadsheet in which data is dumped from a database, there is a dump (on a new tab) for each site.

I need a summary sheet which will add up the two tabs. My problem is however is that I can not use Vlookup as the same codes are used and it will only return the first occurrence.

e.g.
444588 Prime Wages/salaries
This code appears under Production prime labour and Distribution Labour but will only ever return the production prime labour value

Another example would be
444586 Ohd Wages & salaries
This code appears under Production Overhead, Site Overhead, Sales overhead and Admin Overhead this would only ever return the production overhead value only

Is there any way that I can get the summary sheet to use a formula where it looks up the department and then the code? I was thinking index and match but I was unsure if this was possible also.

Worth noting is that the summary sheet has a list of all codes that could be used but the dumps will only ever have values if a cost has been occurred, there for the number of rows in each department is not consistent. There will be a number of tabs however in the attached example I have only provided two.