The problem could well be a line splitter. Do you have filters installed?
Never use BT engineers, as your local high-street telephone repair company will do the trick at less than half the price.
Your main BT socket will have a facia that is split in two parts, any other socket will be an extension. Try the phone in the main socket directly and see if the problem persists.
If it does, and being a BT customer, they have an obligation to repair at no cost.