A soakaway might help.
Dig a hole about 2/3 ft. square and as deep as you can manage positioned at
the lowest point in the garden where the water collects. Fill it with
rubble, brickbats stones etc.
Also dig small trenches leading from several parts of the garden leading to
the soakaway and line these with land drains. (usually available at builders
merchants). If you get it right you will find a vast improvement as the bulk
of surplus water will drain to the soakaway. It is hard work but you only
need to do it once, the alternative being to grow watercress!
Jim