I've done some more investigation this morning, and I think I've narrowed down the problem slightly further. It seems I *can* upgrade 'dkms' (and also install 'shim'), as long as I leave 'shim-signed' uninstalled, although this has a few caveats...
It seems if I 'sudo apt-get purge bcmwl-kernel-source && sudo apt-get install bcmwl-kernel-source' while the 'shim-signed' package is installed, then this builds a "broken" 'wl' module which always gives the message 'modprobe: ERROR: could not insert 'wl': Package not installed' when you try to modprobe it (even after purging 'shim-signed' and rebooting). However if I 'sudo apt-get purge bcmwl-kernel-source && sudo apt-get install bcmwl-kernel-source' while the 'shim-signed' package is NOT installed, then this builds a 'wl' module which works (even after installing 'shim-signed'). I also updated the BIOS on my XPS 13 9343 to version A19, but this made no difference. Because installing or uninstalling 'shim-signed' doesn't automatically rebuild DKMS modules, this means you can easily get into some confusing "conflicting" states, e.g. you can purge-and-install 'bcmwl-kernel- source' while 'shim-signed' isn't installed (to get a working 'wl' module), and then install 'shim-signed', and your WiFi will remain working (with the old module), but the next time your DKMS modules get rebuilt your WiFi will suddenly stop working (with the newly-built module). I know very little about kernel modules and secureboot, but from what I can tell this is possibly a regression caused by https://bugs.launchpad.net/ubuntu/+source/shim-signed/+bug/1748983 interacting with e.g. https://bugs.launchpad.net/ubuntu/+source/bcmwl/+bug/1572659 ** Also affects: shim-signed (Ubuntu) Importance: Undecided Status: New -- You received this bug notification because you are a member of Kernel Packages, which is subscribed to bcmwl in Ubuntu. https://bugs.launchpad.net/bugs/1818134 Title: modprobe: ERROR: could not insert 'wl': Package not installed ubuntu14.04.5LTS kernel 3.13.0-165-generic Status in bcmwl package in Ubuntu: Confirmed Status in shim-signed package in Ubuntu: New Bug description: when installing bcmwl-kernel-source to build wl.ko package version: 6.30.223.248+bdcom-0ubuntu0.2 Expected behavior: kernel module wl.ko loads. What happened: finit_module returns ENOPKG My device is: BCM4352 [14e4:43b1] (rev 03) Happened after latest OS update, downgrading kernel to 164 did not fix, downgrading package did not work. secure boot mode is off. A few others are having this issue https://ubuntuforums.org/showthread.php?t=2413303 There is a possibility it is a modaliases problem -- 2015 chagelog states that there was a capitalization problem, but I don't know how to check this. To manage notifications about this bug go to: https://bugs.launchpad.net/ubuntu/+source/bcmwl/+bug/1818134/+subscriptions -- Mailing list: https://launchpad.net/~kernel-packages Post to : kernel-packages@lists.launchpad.net Unsubscribe : https://launchpad.net/~kernel-packages More help : https://help.launchpad.net/ListHelp