I have decided that the best approach will be to start a deep trench at one end, taking out all the roots I find, then gradually moving the trench along the plot until the whole lot is cleared.
Meantime I have trenched all along the path that separates the 2 plots to try to stop the roots making their way onto the good plot.
We are allowed to have bonfires from next month so at least I will have a way of getting rid of the mass of roots I will end up with.
Plus a little time spent making the original plot tidy...