Have you done the "Log out machine" fix that people have referred to?
I did try that the other day, but it didn't work.
Today I re-updated via Steam ( no idea why steam still thought it needed updating, but it did it twice! ) - it made no difference.
So I logged out of the launcher and logged back in again - this time it actually did the verify code stuff and FINALLY I was able to connect.
Now I need to repeat that process for my other 2 accounts since Frontier are happy to sell you multiple accounts and insist on making the game require a crappy launcher that has literally NO useful features!!! and obviously no support for multiple accounts.
UPDATE - now I have done the whole logout, login, verify, copy user.config file etc for all 3 accounts, I can actually play the game again, but my lunch hour is over so I can't.