The London Film Critics (much like the American critics with the Oscars) do no vote for the BAFTAs (the British Academy Awards). However, much like the American Film Critics, what they vote for can be quite telling of what it is they support.
For a film like Blue Is the Warmest Color to land amongst the Best Picture race can either be shrugged off as a "critics' pick", or you can see that there is support for it that will not only carry into the BAFTA's, but the Oscars when it comes time for the "British contingent" to cast their votes. While it will not likely end up amongst the Best Picture nominees, its place in Foreign Film is almost assured, after there were some doubts as to whether or not the film's explicit sexuality would turn off voters.