Interesting. On mine 'Install connection profile' appears between 'Update log-in details' and 'About the app'. I don't suppose it'll help, but you could try deleting and reinstalling the app.
In turned out that my username was so old it pre dated the time when an email address was introduced to be a username.
As mine was just rogercuthbert it didnt provide all options.
A quick call to the BT WIFI help desk and changing to my email address as the username and hey presto I have the option to download the profile and all now works fine.
If your username for BT is not an email address you wont get access to internet via BT FON. You can change it over the phone with the BT WIFI support team.