It could be a faulty home hub, have you got another one to try?
Otherwise the broadband technical helpdesk will be able to organise an engineer visit for you.
See if your exchange code shows up on this page https://status.zen.co.uk/broadband/
This tends to give more info that the BT one, and may indicate what the problem is.
Are you able to beg, steal or borrow a BT Homehub 5 or 6 and try connecting that. It will at least rule out or in a faulty hub which might speed up getting one delivered if it is faulty.
You could always buy a VDSL Modem/router from your local computer store and try it. Once testing is over, take it back for a refund. Not ethical but you wouldn't be the first to do that.