You can go into your bank with a payment slip, too, and make the payment direct from your account if you feel more comfortable doing it that way - but I too was very hesitant about on-line banking until I got used to it.
My bank has a web page for making payments to third parties, with sections where you enter the recipient's bank account number and sort code, and any reference number relating to the transaction (e.g. invoice number). I pay nearly all my bills that way now.