I have been using this method for ages with no problems. All the customer needs is your sort code and account number, when they go online to pay or into their branch they either tell the cashier what reference to use, (I ask for address) or in the case of online there is a field for them to fill in.
The one thing I would advice though is to use a separate account just for this purpose. It has nothing to do with security as no one can do anything other than put money into your account with just your sort code and account number but having a separate account makes keeping track so much easier, otherwise when you get like me and have dozens of transactions a week it get complicated if they are mixed in with your day to day banking.
I just go down the list once a week and check off who has paid then transfer to the main account. Simple!