Wifi access point login page everytime I open the browser via an intent
Found it.  When I say "e.g. Flipboard", it is only Flipboard that has the problem.

If I clear data on Flipboard, it stops happening.  I went back to the same store and repeated the process of accessing the AP but not completing the logon, and it came right back.  Cleared Flipboard data and all good.

I've bugged it with them.