BT do offer one, its here Download free VPN software - You need to be logged into BT Wifi first
Any description of what that is and whether it's available for other platforms than windows? I mostly use my VPN from my iPhone.
From what I remember, its only for Windows computers, assuming the file still exists.
Also see https://www.btwifi.co.uk/help/security/
it seems all links in this thread are old/broken is there a new or better way to access VPN while on a hotspot.