Few things you could do:
Put a french drain down the bad side of the lawn. Which is basically a trench filled with gravel. You might also want to line the trench with landscaping membrane, this will help stop the gravel getting contaminated with soil.
After forking fill the holes with sand to help with drainage, otherwise the holes will just close backup and you're back where you started. Plus when you use the fork rotate the handle in a circular motion to make the holes a little bigger or get a lawn aerator;
http://www.diytools.co.uk/diy/Main/s...ne-aerator.asp
and save the best till last, a bog garden
http://www.rhs.org.uk/Advice/profile...og_gardens.asp
quote
Bog gardens
A bog garden can be built from scratch, as a conversion from a redundant pond or a
naturally waterlogged depression, to give a pond an informal edge or to create a wildlife garden as a stand-alone soft feature.