This may not be the answer for you, but it seems like a good place to offer my recent experience. We have just added to BT Infinity to our phone package and had no luck at all trying to login to BTWifi-with-FON. After about 5 hours of online chat and phone calls, everything seems to be sorted now.
Our problem was that our BT ID that we created many years ago was not in the form of an email address, which was OK back then. You must have an email format BT ID to use BTWifi and, I guess, BT Infinity. It seems at least 90% of BT chat representatives and the online order system do not know this. The exceptional chap who realised this, told me that there was no way to get a new ID in less than maybe 20 days and recommended we wait until our broadband has been switched on.
So I rang the "check my order" helpline 0800 800150, who were superbly helpful. The first person I spoke too had the right idea of getting me to create a new ID, but that didn't work because it only created a secondary ID. The second person solved it by deleting both old and new IDs and then walking me through creating another new ID, which became the Primary ID. The only downside (I hope!) is that we have lost the bill history in the old ID. We can now use BTWifi-with-FON.
It may be that the BTWifi hotspot you are trying to connect to is not working correctly. If that is the case there is nothing you or BT can do about it. It would need the owner of the hotspot to reset his/her Homehub and this is out side the control of BT.
You will need to find another BTWifi hotspot and try connecting to that to ensure there is not a problem with your log on details.