Colours washed out on rendered video

I have a composition that looks and previews fine within After Effects, however when I render out the video as h.264, the colour looks washed out when I play the video in all but one of my video players (Windows Media Player seems to display the colours fine).

If I export the file a lossless AVI however, the colour looks perfect. I can't use AVI though as this generates a file in excess of 50 gig, instead of the 200 meg h.264 version.

I am sure this has something to do with colour management, but being a complete newbie in that area I'm not really sure what I need to do.

Can someone give me some tips as to how to fix this problem please?