I am a fool, but a lucky one. I locked myself out of my HMRC account earlier, by using my "Activation Code" instead of my password.
So I watched a few bits on the i-player, then went back to my submission, and this time it worked!
Phew! Under 30 mins to midnight.
If anyone failed to log in earlier, do try again before midnight, as you might have left enough time.
You need:
-User ID (12-digits), from Government Gateway card
-password (you can re-apply for this online)
-Activation Code (alphanumeric thing)