I would guess that it is because you are using thunderbird portable which runs from a portable drive, but your OS has no idea about that.

You might get more info if you asked on their forum as you are using one of their products. http://portableapps.com/support/thunderbird_portable

http://kb.mozillazine.org/Running_from_a_USB_drive_%28Thunderbird%29

Yeah I've asked in there too but if the issue was about it being portable surely it would never open the link, not juts when the program was closed.

re :If Thunderbird v38.3.0 portable is closed and I click on an email link I get a pop up window asking me to open a new newsgroup account.

If portable exe file is closed, computer has no idea about it because it is not on the computer, it is on an external device. So, it is locating the only one it knows about. It is using a thunderbird.exe file on your computer; probably in Program Files or Program files(x86) and discovering there is no mail accounts in that profile, hence you are asked to create an account.

I have just reinstalled Windows. There is no installation of Thunderbird other than the portable one.

I have no idea how portable apps work, but I would assume their wrapper that makes apps portable updates the Windows registry on the fly for things like the Default email application. It probably reverses those updates when the program closes. as a portable app that leaves settings everywhere it is executed can hardly be considered portable.