No. XRaySpex is correct.
If you migrate out then I believe you get a short period to move the landline away as well. I suggest you look into the Post Office landline service to see how its costs compare. It's only a monthly contract as well.
You would be able to have Infinity on that. That's assuming your line qualifies for Infinity, which is not guaranteed by the current speed.
You need to check what is reported for your number by this checker
if you haven't already done so. Or the Infinity checker is nearly as reliable if you have already checked there.
If my first link shows an FTTC estimate below 15Mbps then you will get a Not available
from the Infinity checker and you will not be able to order Infinity from BT, though you can order FTTC from several other providers. From BT you could have "Broadband Option 3 with Fibre" if you find a salesperson who fully understands what you are asking for. Many do not - for example see this thread
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost
. Internet connection -
IDNet Home Starter Fibre. Live BQM
"Where talent is a dwarf, self-esteem is a giant."
- Jean-Antoine Petit-Senn.