Swampy beds of doom...

I took on my first ever plot in late March and since then you've probably noticed it's rained a bit.

The plot's on a slope, running from the top left of the plot diagonally down to the bottom right. The elevation is about 3-4ft. The inherited raised beds seem to be sunk into the plot and there are small trenches dug on the right-hand ends, as well as trenches around the mounds of grass that used to be beds/piles of random stuff.

The trenches are all full, and the two 'raised' beds at the bottom of the plot are absolutely sodden. The worst is one bed higher than the one on the bottom border. I tried digging it and rapidly had a pool of standing water. There is a hard pan of orange clay just about 1 spade depth down. The water is going nowhere, despite trenches.

All my neighbours have woodchip paths, mine is the only one with grass still. My next neighbour along has a lower plot than I, but not the same waterlogging issues. I obviously don't want her to suffer from my water surplus, but have been thinking of asking to dig a drainage trench along the length of her plot to drain from mine.

What's the best option to get it drier more quickly (breaking up the hard pan is beyond my back)? Dig a hole for a pond in the bottom right corner? Plant a small fruit tree (or will this drown?)? give up and plant watercress?

Am attaching a pic of how it was in March. The brambles and the blackthorn at the top are now gone. 

Any ideas? I'm very new to all this and the constant mud is 'challenging'!
Thanks
Surbie

Thank you!

Will have a think about those - and definitely consider raising the beds & putting in a pond. I've only had the plot for 4 months, so I don't know if this happens all the time or just this mightily wet year.

Went up to the plot today and quagmire is the least wet word I can think of to describe it. Am amazed the cucumbers are still alive!