Have you got a lawn?
My approach would be
Get a small hatchet and lop off the brambles just below where the lumpy bit meets the roots. That normally stops them cold
Sprinkle on some lime - really it should be dolomitic limestone mixed 1:4 with gypsum.
Pile on ANYTHING which will rot down, weeds, strimmed stuff. lawnmowings, muck, newspapers, old straw, cardboard,etc etc Not sawdust as it will take too long
When it is heaped to about a couple of feet or more then put on your polythene. If it is too thin then double it over.
Peg and weight it down securely round the edges so light doesnt get in
Leave till late spring and you should find it rotted down and able to plant. There may still be some deep rooted perennials, but the soil will be so soft from the worms it won't be too hard work to dig them out.
If you don't have time in the spring to work it cut holes and plant potatoes, encouraging the haulms to come through the polythene. When you harvest you will automatically be turning the soil. Digging is a needless waste of energy in proper system.