Thanks for all the really useful replies - much appreciated!
I didn't know (a) that it was a co-ax socket not a phone socket for the fibre connection (I've only had landline b/b before), nor (b) that you could have only one router per 'connection' (although I suppose it's obvious if you think about it!).
Basically, if I could get both PCs online via the existing router I wouldn't need to get my own, and would happily continue paying my housemate a tenner a month for a share of his.
However, his router is in his room upstairs, while my PCs are on the ground floor, which pretty much rules out running a cable. Also, he works all hours as a sous chef so it's not easy to ask him if I can physically connect and log in to his router to change any settings (even if I did know what to do, which I don't).
AdrianPH's reply did suggest that I'd only been "given router access on a guest account which would be restricted to one Mac address". However, a third housemate (also on the ground floor) has wireless access, so it must be possible to connect several PCs, which implies to me that it's a configuration issue on the Win 7 PC itself.
I just don't get why it won't connect. All I needed for the Win 10 PC was the SSID and password; the network showed in the list, I clicked 'Connect', entered the password, and that was it - internet wireless access.
On the Win 7 PC, if I set the security type to WPA2-Personal (i.e. what the Win 10 say it's using), the SSID is in the list of available networks but has a red X against it instead of the green 'signal strength' bars, and the 'Connect' button is greyed out with a message to the effect that the connection settings are invalid/do not match. If I change the security type for the connection profile on the PC to 802.11, I get green bars and an active 'Connect' button, but clicking it prompts for a username as well as a password, which (as I've said) the router's owner claims not to know.
ukhardy07 asked "Are there two SSIDs, one with 2G and one with 5G?". Apparently there are (I've not actually seen the router, so don't know what type it is) - he gave me two SSID's, "VMnnnnn-2G" and "VMnnnnn-5G", saying not to use the 5G unless I had problems with the 2G. However, the 5G doesn't appear in the list of available networks on either PC.
I'm hoping this is what I call a "Simon says" issue (i.e. you didn't say "Simon says
connect to the router"), where one simple change to how I'm doing what I'm doing fixes it. Any further help would be greatly appreciated, so thanks in advance.
"Weaselling out of things is what separates us from the animals...except the weasel"