I would suggest that you bite the bullet and dig it over with a spade; making a trench at one end and turn the spit of soil over, turning the top upside down to bury the annual weeds and look to take the perennial weeds out by hand. If you can't manage to do all of it at the moment then cover the vacant land with black plastic or old carpet. A large crop of potatoes would be best for one plot and something different for another. This will give you some encouragement to see at least two of the beds producing a crop.

I was going to suggest black plastic too. I was given some of the plastic they wrap hay bales in these days and it was down for over a year. Even tough weeds like rosebay willowherb disappeared.

Thanks for your replies, I have ordered some black plastic and hope for the best next year

Alan