We're sorry to hear that you are still having issues with this.
Our support with third party equipment is limited I'm afraid. As your connection is working with our devices, we can only assume the issue relates to the printer itself. We do have a Gadget Rescue team who could help but this will be chargeable.
The Community may also be able to offer further assistance.
This is not something we are able to assist with here. I have however been able to access your details on our systems and I can see your hub has been running for a long time. Please try rebooting your device as this can clear temporary errors and let me know if the connection issue persists?
Update to my issue. I had HP printer support from Ireland for two hours about 3 days ago. We tried removing/adding web services again, but using my phone as the internet access point, i.e. taking the Virgin Media router/network kit out of the picture, as I have a phone from EE. We had problems connecting via Bluetooth, so had to abandon the test, but it is an option. The problem has always been that once web services was enabled, it looked initially all was fine, even the "Printer connection to HP Connected" = connected was fine... for about a minute or two. Every time tried to print the "Print info page" nothing would be printed, and the summary "Printer connection to HP Connected" would show un-connected.
FIX = A factory reset of the printer worked. After a factory reset, enabling web-services, I was then finally able to print "Print info page", which gives you the "claim code" to add your device to "hp connected services" .... PHEW .. So NOTHING to do with ports being blocked at all.
Tried that (factory retest from menu) and then connected printer to my phone hotspot but still getting message need to roll onto Instant Ink to print and when you get the code still get the above message
Did a factory reset whilst connected via cable. Using the phone as a hotpsot, and tuning off the WiFi (else you are back to using your own virgin media ISP for internet access), took far, far too long .. indeed it timed out trying to download the latest firmware patches (which is a requirement for instant ink service). So the decision was to perform a factory reset whilst connected via the cable.