Hi Alex,
Congrats on getting your plot and welcome to the forum. It might be worth adding your location onto your profile on here so people can offer more local knowledge.
You have my sympathies with your predicament! I have taken over two plots in June of different years and share the same soil type as yourself! I have just taken on another small 2 rod plot and if you check out my blog on this website (link in my signature), I show how I am using lasagne gardening again to create beds as my soil is so rock solid to dig. I would recommend it if you want to get a harvest from your plot before the winter rains make it more spade-friendly and want to save your back!
I also invested in a large roll of weed suppressant bought online which has done me two years and is still going - I use it to cover the paths, covered in bark chippings and also use it to cover sections to weaken the weed growth or prevent new weeds growing before I cultivate. After clearing the weeds, I also recommend laying newspaper and mulching with grass clippings or home-made compost to keep the weeds down. You can wet the newspaper and plant small plants direct in the newspaper and the paper will continue to keep the weeds down.
Ensure you add as much manure on top of the soil before winter. If you do want to dig, it is worth adding grit into the soil to help open up the structure more.
Turning an overgrown plot into something productive is hard work, but is worth it once you can get on top of it. Try not to do too much - do what you can, cover the bit you can't do to weaken the weeds as mentioned. Concentrate on getting a small area cleared and planted before moving onto the next bit. You will get there. Good luck with the plot.