Openreach no longer supply modems.
If you are sure that its not a problem with your phone line, like noise on the line, then try a third party router instead, as they generally give no problems at all.
Here are a couple of suggestions.
TP-Link AC1200 Wireless Dual Band VDSL/ADSL about £67
If you only want single band wireless, then this one.
The TP-Link TD-W9970 for about £40 or less.
They both work will all BT services, including BT YouView.
I mentioned about the W9970 on your last thread.
it appears unsual to get exactly same problems with the hh5 and the hh6 and more like suggest a line or conenction fault many on the forum use a tplink router and have no problems but reading the tplink forum they also have problems just like any other ISP forum
As @imjolly has said, you need to make sure that you have no issues with your line. Although the TP Link is less sensitive to line noise, it will still drop out if there are a lot of errors.
If its just a wireless connection issue, then a different router should help.
Is there any noise on your phone calls? Dial 17070 and select option 2, there should be no noise between the announcements.
@Keith_Beddoe if just a wirelss problem then as I have posted before I find from personal experience the sh6 is better overall that the more expensive dual band tplink VR2600