I think, for those of us with unstable internet, the Openreach infrastructure monopoly is the root of the problem.
We have had over a year of various broadband droputs, router refusal to synch, 0 Mbps download coming into the house on etheret connected computer etc, etc. Some really helpful BT employees and some who tried to deflect the issues. Mulitple Openreach visits arranged by BT.
The result? Openreach say our home wiring etc is OK (repeatedly checked) , the cabinet and exchange are OK, no REIN problem. BT say our connection is perfect even when we send screenshots of the 0Mbps events and outage logs no-one at BT / Openreach can diagnose the problem. Of course the BT Wholesale Speed Checker depends on an onternet connection so is often useless to show the recorded 0 Mbps downlad that shows as the outage starts to recede. In addition as the service slowly returns the "further diagnostics" on that site simply times out because of slow connection.
So we get a good 36 Mbps / 6 Mbps most of the time and then 5 - 6 times a week it simply goes to 0 Mbps for 20-40 minutes at a time with a blue light on the router. Smarthub was worse for this but the HH5 we replaced it with is better but not entirely stable.
Opnereach having the infrastructure monopoly (Virgin fibre is not available here) means that any other ISP risks having the same issues and Openreach have no real reason or motivation to deliver a better service. As consumers our choice is internet via Openreach or no internet. And of course Openreach is not directly contactable or acocuntable to residential customers and so is shielded from consumer pressure. Openreach have often arrived with no idea of what the issue is - surely a basic if you are coming to troubleshoot. BT have told us they can't reliably ensure that Openreach engineers arrive with any form of notes for the job "beause it goes offshore" ?!
We have simply given up after prolonged and extended co-operation with BT and have concluded that OFCOM should not only look at speed delivered but reliability and stability. When it works our broadband is fantastic - when it doesn't work we are told by BT it is working fine. (We exclude any wifi issues from htis situation as they are understandably our reposnsibility - not BT's).
I think until Openreach is either accountable to an external body or has real infrastructure competition in more locations UK broadband reliability is going to be a problem.
A blue light on the home hub, and no Internet connection, would indicate an issue with the home hub, as faults on the external network would cause a flashing light, and noise on your landline phone.
Its sounds very similar to this post https://community.bt.com/t5/Home-setup-Wi-Fi-network/HELP-HH6-blue-light-but-no-internet/td-p/188242...
it does sound like same problem but that was solved by removing an old switch and not by replacing the router although the customer had bought a tplink and decided to use that in preference to the hub