They've been rolling out IPv6 for some time. For the most part unless you actively try to go to an IPv6 site then you won't see any difference. Thinkbroadband run IPv6 versions of the speedtester and I think possibly the site as well so you can tinker with that.
Ultimately this is a step along the path to a move to IPv6 in general. Until there gets to be a wave of ISPs and web hosts moving to IPv6 then it will never happen - BT are doing their bit in not being a blocker to the new protocol coming in to wider use.
However, without concerted international effort little will really change as we keep finding new ways to live with the limitations of IPv4.