I am selling something privately to someone up north.
How secure is a BACS transfer?
Is it free?
What are the other options?
As a seller, BACS transfer is an excellent way to receive payment. It's free, reasonably quick, and has a (practically) zero chance of a Paypal style "chargeback".
As Mal has said, there's no reason to be nervous about giving out your account number and sort code. They are printed on every cheque you write and, in isolation, are of very little use to anyone who has malicious intent.
Many banks now use the Faster Payments System to send/receive funds which would previously have been processed via BACS, so you may even find your money arriving in 5 minutes flat.