vlookup then count? (2000 sr1)

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Sorry, it’s Monday and I’m brain-dead.
I have a list called ‘postcodes’. It has two columns, postcodes and an associated geographical area, an electoral ward. The list is about 10,000 records long.
On a separate sheet, to analyse a service-user survey, a postcode from the survey form is entered, and returns in an adjacent column the corresponding ward from the lookup list .
The results look like
Aston
Harborne
Edgbaston, &c.
I want to count the occurences of each ward. I had in mind to use a formula like
=countif(list,”Aston”), etc.
This doesn’t work because what looks like ‘Aston’ isn’t the text string A-s-t-o-n but the result of a formula.
For the life of me, I can’t see how to do this.
Paste special as values works but is tedious.
=Text only works for strings which look like something to do with numbers.
Idea, please?
Thanks!

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COUNTIF should work with the result of formulas too. See attached workbook.

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Thanks v much, Hans.
Brain now back in gear, helped by your prompt.

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