You could use the countif function.
In a new column on sheet 1 insert
=(COUNTIF($X$n1:$X$n2,Yn3))
=(COUNTIF($X$n1:$X$n2,Yn4))
=(COUNTIF($X$n1:$X$n2,Yn5))
etc.
Fill Down the whole column.
Where X and n1 is the cell reference of the first cell in your column of postcodes in your second sheet and X and n2 is the the cell reference of the last cell in your column of postcodes in your second sheet. The dollar signs fix the cell references so that the range stays consistent.
Yn3, Yn4, Yn5 should be the first, second & third (and so on) cell references of your postcodes in sheet 1.
The function will then return the number of times that a postcode in the column on sheet 1 appears in the column on sheet 2.