Which version of BTHomeHub are you using? As mentioned earlier some older ones probably won't work with the multicast service. Does your order show as completed?
It's not really possible for us customers to tell you whether you can get it or not. BT have started this service in their normal manner, with no fanfare and a total lack of clarity. The customers are confused, the sales reps are confused and even the tech support are confused. I haven't even seen any official BT information saying that it uses the Copper Multicast service.
It might be the case that even though the exchange can support both Fibre Multicast and Copper Multicast for lines BT Consumer (your ISP) has only paid BT Wholesale for the Fibre Multicast service at that location? That's assuming they are paid for separately, which might be totally wrong.
Another possibility is that both services are covered by a single payment from BT Consumer but they want customers in that area to take up Infinity so don't allow the Copper Multicast to be used? Possibly the BT Sport streams are different on the two multicast services and BT Consumer have only implemented them on the Fibre Multicast service at that exchange. Possibly the same BT Sport streams are shared across the two services but BT are blocking customers using them on Copper Multicast at that exchange.
It's even possible that Infinity is available but the exchange supports neither Copper or Fibre Multicast?
Of course the other explanation is that BT just haven't sent your box the necessary software update, or haven't set up your account entitlements properly for the new service.
Who knows? As you can see, I don't know the answers. Only BT know the secrets.