I have the same problem and I am now of the opinion that I just have to live
with it. The only thing that kills it in my garden is a very hard frost. I
have attacked it with Sodium Chlorate (which kills the grass as well) . The
grass tends to come back on its own (in small areas) but the MYOB will not
be far behind.

I have it in patches all over the garden (it was there when I moved in). It
is in the rockery, the borders, and the lawn. It does seem to thrive best in
the damp sheltered areas. It is easy to remove by the handful but as you say
it just grows back.

There is an interesting point in the BBC link posted by Emrys about bruising
the foliage first. I will give that ago. I also intend to grow the grass a
bit longer this year to try and drive out the moss, I wonder if overcrowding
will work.

regards
AndyP