A 2 pair connection on pins 1/2 and 3/6 is sufficient for 100 Mbit/s Ethernet but not faster. Gigabit Ethernet needs all four pairs.
VDSL2 Profile 17a, which Openreach currently use for FTTC, has a raw data rate maximum of around 250 Mbit/s split between upstream and downstream. Without getting too mired down in detail, it's possible for short lines to manage a small amount over 100 Mbit/s in the downstream direction on the current setup, but Openreach do not currently market any FTTC services faster than 80/20 Mbit/s. The current Openreach modems only have 100 Mbit/s Ethernet ports.
It's possible that Openreach FTTC may move to Profile 30a in the future, with a raw data rate maximum of just over 400 Mbit/s split between upstream and downstream. This is by no means certain to happen, as the costs may outweigh the benefits. I believe all the current Openreach modems lack Profile 30a support, and most if not all of the currently deployed line cards in the cabinets lack Profile 30a support. It is only the best quality lines, usually the shortest ones, that will gain a significant speed boost from Profile 30a. Any Profile 30a equipment is likely to use Gigabit Ethernet.
I'm not sure whether Profile 17a and Profile 30a can run side by side on the same infrastructure. Openreach currently use the B8-11 band plan with the optional US0 band specified (BT SIN 498 paragraph A1.1.1 refers). The Profile 30a B8-16 band plan looks compatible, but I don't have a deep enough insight into the issues to know whether side by side Profile 17a and 30a operation is practical, especially when you throw in the complications of vectoring.
FTTP equipment already uses Gigabit Ethernet.
Ultimately, a 2 pair cable will prove limiting, but how soon you will meet that limit is uncertain. My FTTC connection runs at the full 80/20 Mbit/s, and I doubt I would notice the difference with a slightly faster connection other than on a speed test.
As you've found, 2 pair cable versus 4 pair cable might be an academic argument anyway, considering that 2 pair cable is likely to be akin to the proverbial rocking horse droppings.
At least some versions of the BT Data Extension Kit used to provide the Home Wiring Solution on FTTC installations were reputed to use 2 pair Category 5e cable. Maybe someone can confirm this, especially whether the kits currently available contain 2 pair cable.