Well I am not on a BT's Business connection, just Infinity 4 using a Smart Hub, but I am having no issues accessing HTTPS (SSL/ TLS encrypted sites) at all.
I do have the odd issue where I have to click on a link twice for the link to work or else the page times out, but that happens of any type of page whether it be HTTP or HTTPS, it might be a browser issue I don't know.
One thing you could check is see if the site in question has a valid Certificate, most browsers now days refuse to access them if they are not signed by a reputable source, i.e. if the site self signs their own certs the browser will tell you or just refuse access to it.
Also some Virus Checks don't like self signed certs as well.
- Infinity 4 - 310Mbps (down), 31Mbps (up)