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All FTTC providers use the same fibre infrastructure - Openreach's - for the local loop. Most with the notable exception of two providers use BTw's backhaul network as well so are at BT's mercy for routing. The two that don't could potentially provide better or worse pings but everyone else will be the near enough the same.

I would find someone near you who is on BT and do a traceroute from their machines to a gaming server. That would give you the baseline of what to expect on BTw. BT aren't bad last I checked but certain LLU providers would be better.

No way of knowing without trying them out in your local area or speaking to someone who has.