BT FTTC means any FTTC service delivered via BT Openreach - not just Infinity / Infinity for Business. If BT Retail products like Infinity are available, any other ISP offering FTTC service via BT Wholesale can offer you FTTC, and if TalkTalk connect their network to the fibre infrastructure at the exchange, so can any TalkTalk reseller.
I'd try to get the most accurate information you can about FTTC availability and possible speed before proceeding further, so that you have a full understanding of the options. Does the BT Wholesale DSL checker
say anything about FTTC or FTTP? Search by phone number if that works, otherwise by address. The postcode only checker tends to omit FTTC and FTTP even when it is planned or available.
If BT FTTx is an option, I would argue it's a better choice than Virgin Media for jitter sensitive services like VoIP. I consistently get the maximum possible MOS score of 4.2 when simulating 5 G.711 calls on the Visualware VoIP simulator
- just now my result was MOS 4.2, no packet loss and 0.3ms jitter
Whichever option you go for, I don't think you'll get out of paying for a phone line. A phone line appears to be mandatory for the Virgin small business products, whilst you will need a phone line for FTTC. You may persuade a business FTTC provider to rent a copper pair from BT Openreach and not bother to put voice service on it, though this kind of 'naked DSL' service is not common.