All of what Yorkie said RE: not running afoul of local/national authorities - do that, regardless of what else you do.
A simple way to fix drainage problems (if approved) is a French drain
https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://en.wikipedia.org/wiki/French_drain&ved=2ahUKEwj16eKt7Y6KAxW4mYQIHbrbN1sQFnoECA0QAQ&usg=AOvVaw2xP59p7uP2Obq8NJ3WGE7s Dig a shallow trench, maybe 12 inches deep, sloped to a collection/discharge point (such as a ditch or stormwater drain. . . again, if approved). the bottom of the trench should slope gently toward the collection point. place a base layer of
coarse sand, or small gravel. Make some perforations in some PVC pipe, smaller holes than the sand/gravel you use. Lay the pipe in the trench on top of the sand/gravel, the discharge end of the pipe remains open to the ditch (etc.), the up slope end should be capped. Place more sand/gravel to cover the pipe (for a garden I would fill up to 6 inches deep). Place some porous landscape fabric over the sand, fill the remainder with your garden soil. Mark where buried drains are located so gardening does not dig them up. The work can be done by hand / allotmenteers, or done professionally. They do work.
Good luck with whichever drainage method you choose!