will FTTC only be available from BT, or will other suppliers be able to use their infrastructure?
No "will" about it. Though BT Infinity seems to be the cheapest - trying to freeze out the competition at the start. The BT ads on TV are also misleading in many people's opinion.
Infinity is BT Brooadband's FTTC offering, the underlying FTTC itself product itself being Openreach, and BT Wholesale then providing exchange and backhaul just like ADSL Max and 21CN WBC. (So yes, the infrastructure you refer to).
Any ISP that wants to can supply the BT Wholesale service, just like ADSL and ADSL2+
The ones providing BT Wholesale FTTC so far are in this list
. There are no LLU suppliers but TalkTalk is supposed to be doing that soon.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost
. Internet connection -