To get reasonable performance you'll need to import the PAF into a
database table and index it on the postcode, if you haven't already done
so.
After that, most applications seem to have a textbox or combobox for the
user to enter the postcode. (If a combobox, use Allen Browne's technique
for dealing with comboboxes with large numbers of records in the
rowsource: you'll find it somewhere at
www.allenbrowne.com.)
Once a postcode has been entered, the usual system is to use it in a
query to populate a listbox or combobox with all the addresses that
match the postcode. If the user finds the desired address in this list,
they click on it and then use this data (with maybe a further query to
return all the fields in the one record you're interested in) to
populate the address fields in your record.
If the desired address isn't in the list, take appropriate action: e.g.
allow the user to type it directly into the address fields and flag the
record for manual examination later.