I'd suggest putting in raised beds, where its waterlogged the most. Springs on its way, plenty of skips will be sited on roads and lanes across the land, plenty of good wood being thrown out. This is how I get my timber - skip shopping, it's great. Do ask permission first though, just to be polite.
You might find the ground will start to dry out a little. If things didn't improve over summer, then think of other ways to resolve matters.