BT will NOT sell you Infinity with that sort of speed, however, they do have a "Faster Broadband" option which uses FTTC and is aimed at sub-15Mbps lines.
That might not be exactly true.
If it was not viable to sell the fibre product at that speed then it most of the time would be hidden and would say on the BTOR Where and when page that its out of reach.
But where its still listed they should be able to buy it, its better than they current ADSLx so its an improvement, I am sure BTW would still be happy to get some revenue for their fibre product to pay for its cost of installing it.
But that just my opinion.