maybe in the past they have had a bonfire on that part of the plot and burnt plastic and such like may have tainted the soil 
No. It was the whole plot. It was seriously weed infested, particularly bindweed, docks and others. I tried growing plants further down the plot, put in new rhubarb crowns - they died. Neighbour gave me some of his rhubarb crowns, planted them at the opposite end, they died. Dug them up and they were rotten. Even my runner beans (Scarlett Emperor), the only thing that did produce something, weren't that good a crop, the plants sparse, not many leaves on them.
One of my neighbours at the new plot said that I was wasting my time, effort and money as many of the plots at that end (opposite to where I am now) have very poor soil and little if anything grows, hence even people have had tried for several seasons give up in the end.
New plot I'm on seems to be a lot better. My Rosemary is flourishing, so is the rose I rescued from the vacant, overgrown plot next door (just as well I did as the council came in with their tractor to cut the grass and they would have run the poor thing over and killed it) and couple of lavendar plants I put in are growing. Soil is still clay but seems a lot more friable than the old plot. Apparently the plot I'm on was well looked after until 2-3 years ago when the tenant passed away. I would say that's probably the case as weeds, apart from a patch by the shed which has a fair bit of couch grass on it - which I'm digging up, is relatively weed free. It's grassed over but the roots aren't that deep and just turning it over and letting the sun do the rest seems to be working quite well.
Would have liked to have turned it over before winter set in but son's kidney transplant failed after 6 years, he wasn't feeling very well so the plot had to take a back seat. He's on renal dialysis now and has got a lot of his energy back so is helping out as and when he can.
