Firstly, all ADSL travels over copper - your house is connected to a copper wire all the way to the exchange. The new FTTC stuff extends fibre to a big green box in your street (Fibre to the Cabinet) - still copper into your house tho.
That modem is an ADSL2+ item so it should be capable of speeds upto 24mbps - if it were an older ADSL modem it would have maxed at 512kbps!
The speed you actually get really depends on
a - distance to the exchange
b - quality of connection
c - speed at the exchange
Stick your postcode into a speed checker (all providers have one) and see what your exchange is offering/what you max can be.
Then take a peek at your modem’s connection stats - the things you’re interested in are the Attenuation and Noise figures for the down and upstream connections. They tell you what the quality of the line is like and if there’s room to increase speed on the line.
You might want to make sure you test it on the master socket in the house - and disconnect EVERYTHING else INCLUDING microfilters to do that.
It’s also possible your line has a profile on it to slow it down for some reason but only your ISP can find that our (from BT themselves).
Bottom line - it’s unlikely to be just the modem unless it’s borked - and if you want a new modem, just sign-up with a new provider and you’ll get one!