Problem With Conversion Of String

I have a feeling I'm missing something obvious here, but being new to
SQL Server is my only excuse!

I have a table that holds a variety of data. I am writing a user
report where the user wants to be able to return all data that falls
between a start and end date that they enter.

The query should therefore be along the lines of

SELECT [some columns]
FROM [my_table]
WHERE [column holding date] BETWEEN [start date] AND [end date];

However, the column holding the date information has been defined, for
reasons best known to the designer, as a VARCHAR(10) and the data is
in the format dd/mm/yy.

I have tried CAST, which simply gave an error. I then tried CONVERT
in the form CONVERT(datetime, [column holding date], 3) and the query
runs without error but returns no data, even though I can see there is
data that would meet the criteria in the table.

Can anyone help me with a solution to this?

Thanks

H