Can you post your line stats from the HH5 please? These are in Troubleshooting/Helpdesk on the web interface at http://192.168.1.254
Lines 1-13 will be enough
Do you have written conformation that your speeds will be guaranteed because the speeds are usually not guaranteed. The reason being that there are to many variables involved and speeds can fluctuate.
That is why the ISPs sell the broadband as speeds up to. It is also why the checker that you use is an estimate of the speeds you may get and gives a range of the lowest speed and the highest speed depending on the quality of your line.
As has been pointed out your speed is within the estimated speeds for your line so I doubt BT will do anything to try and improve them for you.
You could try replacing the HH5 https://community.bt.com/t5/BT-Infinity-Speed-Connection/HH5-alternative-modems/td-p/1444549