When you set up direct debits and standing orders this information is needed as it is the branch identifying number to ensure your bills are paid correctly and that you are paid promptly - no scamming - ask your bank to explain
I work in a High Street bank boobesque and I don't think knowing a sort code alone would be of any use to anyone. However, if the same person were able to obtain an account number that was based at that bank, it may be more serious, and if they have the account number they usually have the name also, as they would probably actually have a stolen card or other paperwork.