I don't think that this can be done.
You would be better off to get a second line in and have the 0800 number going to that line.
1. If you are on the phone at home, the business line is not engaged.
2. You can send faxes while you are on the phone using the other line.
3. You can connect the 0800 line to the computer and have it record the details and messages.
4. Someone can send you a fax to the 0800 number and the computer will automatically detect if it is a fax and will pop up on screen and take the fax.