Email Links redirected to ISP router IP address

On all PCs, Android and iOS tablets, and Android phones, many of my links in emails (I use Microsoft Mail, Outlook.com and Gmail) haven't worked for 3 days. The broken ones all have my Hub IP Address and a few more words before "_url=http:// . . ." (then what I assume is the address where I SHOULD have been sent to; deleting the bit before the "=" sign doesn't work.)
Have 'factory reset' router myself, as well as under control of BT Helpdesk, and in fact they eventually sent out a new router (Home Hub 5) today, but the problem still exists.
Problem MAYBE caused by me switching on BT Web Protect for a few hours but I then cancelled it again as it was not the thing I wanted. It is the only event I can remember which involved any of this stuff. I also switched OFF Parental Controls which I have had running for years.
Since it affects so many different devices and email clients, and it presumably isn't the router, is the problem at my ISP i.e. BT? (I have had 5 or 6 calls to them in the last 3 days.)
Some links work OK. But even Verification emails where you just have to click a button in the email to confirm something still take me to the BT Hub Welcome page.

My desktop PC is wired to the router, but everything else is wireless.

Any clues?

Cheers, Nortonian

Open a CMD prompt type

Tracert Adobe.com

Post results check all browsers that you don't have a proxy set and check anything new in startup like security software

Hi
Thanks for the response. I have run tracert adobe.com. Hope it helps you - it is too clever for me!

I have also set to 'Off' PicPick which is a screen grab utility which I loaded in the last 2 weeks.

My Edge, Edge Dev Edn, Google Chrome, Firefox have never had the Proxy settings altered: I uninstalled Firefox, mainly because it displayed a message saying I wasn't signed in to the Network: when I pressed the button to Sign In, it took me to the same crazy page that everything else did!

Thanks again

Please download MINITOOLBOX and run it.
Download MiniToolBox

Checkmark following boxes:

Flush DNS
Reset FF proxy Settings
Reset Ie Proxy Settings
Report IE Proxy Settings
Report FF Proxy Settings
List content of Hosts
List IP configuration
List Winsock Entries
List last 10 Event Viewer log
List Installed Programs
List Users, Partitions and Memory size
List Devices (problems only)
Click Go and post the result.

Hi Samurai
I am going to give your suggestion a try out tomorrow, thank you very much. Someone on the BT Community suggested turning off Smart Setup on the router, and with a very limited amount of testing, that seems to have worked. Here's hoping.
Thank you for your excellent help so far.