I am not aware that you must use a HH. Even their own website states that you can use another modem, but they will not give you technical support for that equipment. ie they wont help you configure it.
Not having a HH installed does not stop them running any fault tests needed prior to reporting to Openreach. They will still be able to perform a GEA Service Test. The only difference is they will know its not their own equipment as it will return:-
"GEA service test completed and [no/fault] found but unable to check for customer equipment connected to the modem".The main site page
Openreach [MCT] Modem Conformance answers a lot of the common questions and list of approved modem/routers which I last updated July 25th 2017.
>> I could see that we only had a s/n margin of around 1-3dB on the downstream,If the SNRm is at time running at 1dB, then its not surprising that the line may be experiencing some problems.
It may be useful to reboot the modem and note what the SNRm is immediately after a resync.
It's not unusual for SNR on some lines to vary over the course of the day, but if it does currently have a Target SNRm of 3dB, then I would expect DLM to be taking action and start reversing. Need to know really how much SNRm varies over the course of the day and if its a standard daily spread... or something more attributable to EMI or a HR type fault.