In Britain it's standard practice to use an electronic bank transfer, otherwise known as a "standing order" for the monthly rent payment. Many letting agents insist on it here in Britain. It's rare to hear of fraud. It is possible to setup a Direct Debit with the account numbers, as happened in a famous case where Jeremy Clarkson claimed loosinglosing account numbers wasn't a problem. If a direct debit is taken from your account, then you are protected by the the Direct Debit guarantee which means that you get a full and immediate refund if there is any fraud or unexpected payments spotted.
Some landlords, particularly of bedsits accept plain old cash, however that's not recommended as there is no trace of it being paid, which could lead to legal disputes.