I think there is a bit of confusion about what speeds you should be getting with your package.
Infinity 2 is sold as "up to 76Mbps". This does not mean you will necessarily get that speed. When you signed up BT would have given you a guaranteed minimum speed for your line. This can be any speed up to 76Mbps. If you check the paper work you got when you signed up to BT it should tell you what the minimum guaranteed speed you should expect to get.
One of the main things that affects the speed delivered is the distance from the cabinet to your property.
If your line is only capable of delivering 30Mbps that is all the speed you will get regardless of the fact you are on the Infinity 2 package with an upper speed of 76Mbps. In that instance you would as well being on the Infinity 1 package, which has an up to speed of 52Mbps, which again you would not be able to get but the package would be cheaper.
With FTTC, Fibre to the Cabinet which is what you presently have, hence FTTC, then it is copper wire to your property.
If your area is being offered FTTP, Fibre to the Premises, you would need to order that and have it installed to your property. There is no automatic upgrade to it because as has been pointed out, it is a different product.
Not only that but FTTPoD (on Demand) is a totally different product again, normally used for busnesses with an install charge of anything from £1,500 depending on the distance to the nearest firbre aggregation node. The monthly rental is far higher and a 3 year contract.
As usual BT make it as difficult as possible for non techs to understand what is going on with Broadband.
Having spend 1.5 hours talking with BT in various departments I have discovered by accident that we now have FTTH available to our home.
This is a different product and you have to get stuffed up with a new contract for 18 months with BT. They will provide a fibre cable to your house and install new sockets and a router.
There are other providers with equally good or better deals out there and we are going to one we use at our business premises.
I have tried to get confirmation online about the pricing of 1,2,3,4 which speed range at my house from 55/10 @ £49.99 on the lowest to 300/50 £59.99 on the highest but alas failed so far.
Hope this post is helpful but it does only refer to my personal circumstances.