As you've said, they are not obliged to provide FTTP. There are people on here that have taken a year to get an FTTP install completed.
You could order a standard line, but if there is only fibre at your address, it's likely you'd face thousands in excess construction charges to get a copper line to you, as they only have to cover the first £1,000.
There is no guarantee such a line would be any good for broadband - you'd probably only get ADSL and may be miles from the exchange.
Perhaps if it's urgent, you should look in to 4G to tide you over? EE are doing two months of 100GB a month for £10.
Edit: You've mentioned "without a home phone" several times. I thought BT insisted on providing a FVA line even in these FTTP only areas? Perhaps that is what is preventing BT progressing - you haven't ordered a phone line. Even if this is technically possible, all their usual orders will have a phone number attached and if yours is "weird" it might cause delays.
I do wonder if your address shows availability of Infinity Option 4 (330/30, £50pm) on the BT Retail site, and if ordering that along with the requisite telephone line, would be quicker.
Edited by nemeth782 (Fri 11-Dec-15 17:34:06)