Zen has a really good write up of how the DLM works and you can read up on it here:
For VDSL based connections, your target SNR margin is 6db for most providers, if it's close to 6db there isn't much you can do to increase speed without changing some equipment.
Regarding what you can change, I've found a minor speed bump by going with a twisted pair DSL cable instead of the thin/flat DSL cable that comes with your router. I'm currently using the Tandy (yes they're still in business) DSL cable and that has given me a minor 3mbps boost (though results may vary), remember that shorter is better with these cables.
If your ISP doesn't make a fuss over third party routers, consider swapping the ISP-provided router for either an old Openreach HG612 modem or an Openreach certified modem. The HG612 is quite cheap to obtain and in my experience is rock solid stable and also can be unlocked very easily which will also give you more in detail stats on your DSL connection.
The BT wholesale checker information is only meant to give an approximation of the line's performance and in many cases, you'll get speeds that are slower than what it says. The speed range quote that you get when signing up to broadband is fairly accurate.