‘Marshes’ is somewhat of a misnomer round here.
While back in the day, there was plenty of marshland east of Burnham, now it is mostly reclaimed farmland protected by a seawall, on the riverside of which are, sometimes, saltings or saltmarsh, i.e., marshy areas of marine grassland cut through by rivulets some of which were, long ago, used for collecting salt in mudbeds.
However, as you stride out along Marsh Road (which begins at Saint Mary’s Church) you do encounter a variety of birdlife and the grand feeling of massive skies over a flat landscape. You can walk right down to the sea (around six miles) along various public footpaths.
Please be respectful of the fact that you are surrounded by private farmland, and do, please, bring your rubbish home.