Assign area to postcode from multiple arrays function

Hello,

I'm hoping you can help. I have a list of the first 4 letters of a postcode, and based on a separate list of postcodes, I'd like to return a value of what sector they're from. Here is an example:

Sheet One

1 BB1 1 FORMULA TO WORK OUT SECTOR
2 BB5 2 FORMULA TO WORK OUT SECTOR
3 BL1 2 FORMULA TO WORK OUT SECTOR
4 BL2 2 FORMULA TO WORK OUT SECTOR

Sheet Two

1 Bolton Wigan Salford
2 BL1 1 BB1 1 M6 6
3 BL2 2 BB5 2 M6 1
4 BL3 1
5 BL3 6

Obviously, the real data is more complete than that, but hopefully you get the idea. In 'normal english,' I imagine the formula needs to work something like:
IF A1 matches any of the array in sheet 2, A1 - A5, Then return "Bolton, but if it doesn't, try range in Sheet 2, B1-B5 and if it matches, return Wigan. If it doesn't match that, try the next column etc etc, and if it doesn't match any of the columns, then simply return 'No Sector.

I feel this might be asking too much of excel, especially as the formula will be on each row in the main sheet.

Am I asking too much?

Looking forward to your responses,