I've now fixed this problem. It finally occurred to me that the place to run the printer troubleshooter was not the laptop that couldn't see the printer but the desktop that could. This detected that the printer was not a member of my homegroup and gave me the option to fix it, which I did. Now I was able to reinstall the printer on the laptop and print a test page successfully.

I don't think the printer has ever been part of the homegroup, so I'm guessing that this requirement  has arisen from a recent Windows update, no doubt with the best of intentions to fix a security hole. Pity there was no warning of the effect this might have on unsuspecting folk like me.

Another thought. To find the printer trouble shooter you have to search for it. Searching for 'printer' doesn't find it, as it is called "Finding and fixing printer problems". Someone probably thought this was a helpful name, but if you have to know what it is called to find it, that's not so helpful. Just "printer troubleshooter" would probably have worked better.

I spoke too soon. While access to the printer from my W8 laptop has been solved by joining the printer to a W8 homegroup, I still can't print from my W7 laptop. It seems that there are W8 homegroups and W7 ones, but not mixed ones. This means that my W7 laptop can't join the W8 homegroup that my desktop, printer and other laptop all belong to. 

Is there a way to have mixed W7/W8 homegroups or for a W7 m/c to join a W8 homegroup? Or is there some other way to give my W7 laptop permission to send to the shared printer wirelessly?

I managed to connect via the network to my desktop and thence to the printer, which then appeared on the W7 laptop 'devices and printers' list. Making this the default printer then seems to have solved my problem. 

Thanks to this list. You helped solve my problem just by giving me someone to talk it through with :-)