sorry if this is completely the wrong forum, but I figured someone here would know.

If I've got 3 BT business telephone lines (connected to a PBX system) can I make it so that someone calls our main line phone number and its engaged, the call will be put through on the second or third line? Is this a service that BT can provide? I don't want an 0845 number because that is more expensive from some places, and doesn't work internationally from everywhere. I know that using featureline will do it, is that the only way?

Yes, BT provides it. It is called "group hunting".
This is part of my day job so PM me if you have problems and I will happily guide you through the mire of contacting BT.
We use it for many clients with appropriate busying and bypass.