BT (and others who resell their bandwidth) offer two types of fibre - FTTC (Fibre to the Cabinet) and FTTH/FTTP (Fibre to the House/Premises). FTTC is far more common, but if you're lucky and have the dosh, you may be able to get FTTH, whose bandwidth is effectively unlimited. FTTC relies on your existing copper cabling from the cabinet to the house and the bandwidth is therefore affected by distance from the cabinet just like ordinary ADSL. As a rule of thumb at about two miles from the cabinet there is no point in FTTC, ADSL will be faster.
BT finally got round to putting some fibre cabinets in Portsmouth about this time last year, so I switched from Demon's ADSL to BT's Infinity 1 using FTTC. I'm about two hundred yards from the fibre cabinet and my bandwidth jumped from 3.5Mbps to 38Mbps, a very noticeable difference. It took the Openreach man about fifteen minutes to do the swap, including walking to the cabinet and back!
Just bear in mind that if you're using something like Speedtest to check your bandwidth use a hard-wired connection, not WiFi. There's usually quite a difference in performance.
Andy