Hewlett-Packard C4380 Wireless: Can See, Scan, but not Print. Help!

I am trying to print with an iMac or a Mac mini (both Intel Core 2 Duo) running Leopard 10.5.4. I got a Hewlett-Packard Photosmart C4380 all-in-one recently and the 802.11g printing is the main attraction. In brief, if I network it through my AirPort Extreme it all works fine. But I don't want to do this as I want to reserve the AEx for 802.11n at 5GHz for video on the home network, and I want to use the wireless capability of the router my ISP gave me, a Thompson Speedtouch 780 (with proprietary firmware from O2), so I run them on one network connected by ethernet. This, or a close variant of it, is the wireless router most commonly deployed in the UK, and it works fine with all my other devices (iPhone, PSP, PS3 etc.). With the HP software (9.7.1) on the 802.11g router the C4380 is seen; I can scan; configure; check ink; the works. But what I cannot do it print - I get the following error (in the printer from Print & Fax preferences) after the job appears to have been sent properly:
"Communication Failure: The computer is no longer able to communicate with your printer. Turn the printer off, check your printer connections and check for printer errors, and turn the printer back on."
Signal strength is reported as 5 out of a possible 5 and I have no interfering devices or neighbours on the same band. However, in the HP Printer Utility app if I go to "Print Test Page" it clearly tries, getting as far as the first row of letters and half way through the second before giving up. That seems particularly weird. Again, it prints fine if I point it to the AirPort Extreme instead. (And for that matter USB.)

I have tried disabling any Firewall in router, as well as UPnP. I have tried both Bonjour and direct wireless (I use direct wireless by default). I have the IP address configured to be static. I found in another post some Terminal commands:
sudo chmod -R 775 /Library/Printers/hp
sudo chown -R root:admin /Library/Printers/hp
This seems not to have worked either.

Lastly, this is what I get in the Console under /var/log cups error_log:
I [06/Jul/2008:19:17:33 +0100] [Job 2] Adding start banner page "none".
I [06/Jul/2008:19:17:33 +0100] [Job 2] Adding job file of type application/pdf.
I [06/Jul/2008:19:17:33 +0100] [Job 2] Adding end banner page "none".
I [06/Jul/2008:19:17:33 +0100] [Job 2] Queued on "HP8CFD23" by "<user>".
I [06/Jul/2008:19:17:33 +0100] [Job 2] Started filter /Library/Printers/hp/cups/Photosmart.driver/Contents/MacOS/Photosmart (PID 751)
I [06/Jul/2008:19:17:33 +0100] [Job 2] Started backend /usr/libexec/cups/backend/hpip (PID 752)
E [06/Jul/2008:19:20:08 +0100] PID 752 (/usr/libexec/cups/backend/hpip) stopped with status 1!
I [06/Jul/2008:19:20:08 +0100] Hint: Try setting the LogLevel to "debug" to find out more.
E [06/Jul/2008:19:20:09 +0100] [Job 2] Communication Failure: The computer is no longer able to communicate with your printer. Turn the printer off, check your printer connections and check for printer errors, and turn the printer back on.

I'm really at a loss. I am asking the same question on O2's board (the ISP) as the point of difficulty seems to be the router, but even then I'm not 100% sure. I see the address of the printer is
hpip://192.168.1.66:Photosmart%20C4380%20series/2:0.1e.b.8c.fd.23
I am wondering if the router could be blocking the "hpip://" protocol?

Thanks for any help!