Try to start Windows 10 in safe mode with networking enabled.

Does the problem go away?

Windows safe mode disables anti-virus software. This is a troubleshooting step, not a solution.

I've tried that - twice - but my wifi adapter doesn't work while the PC is in safe mode with networking. Could that be an issue with USB ports?

Looking at my Sent items, and knowing which ones I sent from my phone, it looks like I haven't sent an email from Thunderbird since late on the 7th, so if the problem was caused by an update it could have been a couple of days ago.

Google at least appear to be forcing two factor authentication, or oAuth. You can change the method in account settings, but in your case you will also need to update the server names to the gmail equivalents. The very old and venerable googlemail server names just don't work well with oAuth.

GMail server names and other settings are documented by google here

But that does not explain the bulldoghome issue or probably your specific failure with google. I would suggest you check the Thunderbird settings against those of your provider https://www.serversettings.email/bulldoghome.com-email-server-settings-imap.php#thunderbird THe images on their web site may be somewhat dated, but the server settings, port and security will still be as valid as ever.

You might try disabling any anti virus you have installed. That is the most common cause of sending issues, post opdate. They block the new and unknown software from accessing the internet on mail ports using their firewall component, or have spam/ scam filters that are not compatible with the newer version of Thunderbird.

You should have a wired connection to your wifi adapter as any diagnostics anyone asks you to do with regard to windows and third party software will involve safe mode with networking. While wifi is convenient, I am sure all adaptors come with either a USB or cat5/6 connection for diagnostics.

my wifi adapter doesn't work while the PC is in safe mode with networking.

A wired connection is preferred in safe mode. Alternatively try https://community.spiceworks.com/how_to/125006-how-to-restore-wi-fi-connection-in-windows-10-safe-mode

Google at least appear to be forcing two factor authentication, or oAuth. You can change the method in account settings, but in your case you will also need to update the server names to the gmail equivalents. The very old and venerable googlemail server names just don't work well with oAuth. GMail server names and other settings are documented by google here But that does not explain the bulldoghome issue or probably your specific failure with google. I would suggest you check the Thunderbird settings against those of your provider https://www.serversettings.email/bulldoghome.com-email-server-settings-imap.php#thunderbird THe images on their web site may be somewhat dated, but the server settings, port and security will still be as valid as ever. You might try disabling any anti virus you have installed. That is the most common cause of sending issues, post opdate. They block the new and unknown software from accessing the internet on mail ports using their firewall component, or have spam/ scam filters that are not compatible with the newer version of Thunderbird. You should have a wired connection to your wifi adapter as any diagnostics anyone asks you to do with regard to windows and third party software will involve safe mode with networking. While wifi is convenient, I am sure all adaptors come with either a USB or cat5/6 connection for diagnostics.

Thank you Matt. Due to the coincidence of timing I did initially wonder if it was connected with the Google 2-factor authentification but then I discovered that it affects Bulldog too and I am automatically signed in to Gmail anyway (I don't need the 2-factor authentification until I need to manually sign in) which seemingly rules that out completely, especially as I can still receive mail.

It increasingly looks to me like the problem is connected with a Thunderbird update - the version I'm using was released on 7th December (and probably installed when I opened Thunderbird on the 8th) and I was last definitely able to send emails with Thunderbird on the 7th. So it seems likely to be an incompatibility of this version of Thunderbird with either my AV (although it still didn't seem to work when I tried turning the AV and firewall off as per Thunderbird troubleshooting suggestions) or Windows 10. But if it were the latter, you'd think many thousands would have the same problem - it would be interesting to know if many have. I've certainly had issues with Windows 10 updates not playing nicely with various drivers in the past; they've tended to disappear with further updates though.

Given the geography of the house and location of the comms socket and therefore the router, the necessary length of cable between the PC and the router is 10 meters plus and I'm not very inclined to move it to somewhere near enough to connect it with a shorter cable (it's a tower, not a laptop) so I'm tempted to hope that Eset, Thunderbird or Windows 10 will solve the problem with a further update.

Alternatively try https://community.spiceworks.com/how_to/125006-how-to-restore-wi-fi-connection-in-windows-10-safe-mode

I tried doing that but the only buttons I can see in the logon screen for safe mode are Language, Ease of access and Power.

This is a Windows issue, and beyond the scope of this forum. I'd suggest you do your own research about how to get WiFi going in Windows safe mode.

I'm tempted to wait it out for now to see if a further update solves the problem

Don't hold your breath. My bet would still be on Eset being the culprit.