It's not the soil that's tough. It's the grass that's been growing on it for about 5 years. I've strimmed it all but it's a nightmare to get through. A fork works best but it's going to be very slow going. Think I'll get the weed killer out.
Sounds very similar to our plot except we also had problems because we got the plot in midsummer and the soil was absolutely rock solid - you couldn't get a spade or fork in it! The majority of the plot hadn't been cultivated in living memory!
I didn't really want to use glyphosate as it still needed weeks to work and we took the plot over in mid-June so didn't have this time to spare if we were going to get our monies worth of crops from it that year.
We ended up using the lasagne bed method, covering the grass with cardboard first. We used weed suppressing membrane on the paths and topped the lasagne beds with membrane, planting through this for our squashes, brassicas, etc (which we started off in pots first). Everything did really well because the black membrane helped the fertile stuff in the beds to warm up. We then turned the beds over in winter when the soil softened up and could remove the pernicious weeds which hadn't been killed off by the lasagne bed method.
I then used glyphosate sprayed through the neck of a cut off lemonade bottle over individual weeds in spring time where stuff had sprouted between the paths and new beds.