iPhone does not connect to wifi "hotspots"

My iPhone 4s, 7.1.2, can connect to wifi networks.

But when it detects that wifi network as a "wifi hotspot" (eg, Starbuck in UK) the "connect to a hotspot" thing appears and then nothing else happens - the phone does not join the network. That dialog just times out.

How do I troubleshoot this?

How do I fix this?

I have tried making the phone forget all network settings but that didn't work.