I was playing quite happily until after the credits at the end of Act 3; watched the new intro, then onward to Act 4.

Now the game seems to be working fine, but I can't progress.

I go down a path, I defeat whatever is there, and then I am back at the same menu.

I mean I acquire EP (I've levelled up several times) and so on, but the story doesn't progress. The menu is the same as when Act 4 started.

The only thing I can think of is this: I spent most of Act 3 underlevelled by between 5-12 levels. So I finished Act 4 as a level 73 (Human Mesmer). I've levelled up to 77 now, with no change.

Is there a level I need to be before something happens?

Also, I didn't fight in the Arena much. Is there a minimum level I had to reach there?

(FWIW I am playing on Classic mode.)

ETA: The answer seems to be "Yes". After levelling up to 90 (i.e. 18 levels of pointless grind), the story finally progressed.