Does that mean Fibre To The Case, or something similar? i.e. Fibre to the Green thingymajig, and then copper to the property?
yes
If so, I have been quoted speeds of 38Mb down and 10Mb up with this.
Thats a restricted product - the top whack is currently 76M down, 19 up - obviously what you get is dependent on distance between your house and the cabinet.
I currently receive 20Mb down and 1Mb up on Copper (I'll do the BT speed test thing you suggested when my torrents finish downloading). I'm about 300m from the exchange! 
Forgetting illegal downloads, 20Mb is fast enough for most things - streaming, web etc. So you may not see the benefit.
For me, what really makes FTTC worthwhile is with cloud storage/apps - because the upload is fast, such things become viable. Streaming whats on my media center also works well. Everything is just so much more fluid, and what we all assumed the future internet would be.