Hi nigel,
No need to plough up get some used scaffolding planks sna create some 8×4 ft beds then go to your local bike shop or such and get some cardboard lay on groung and fill with good compost, it will cost a bit at first but there will be few weeds and any roots will easily penetrate the cardboard below.
We did this successfully last year and you can see the results here on our blog https://bifegardencollective.wordpress.com/
No dig is the mantra and it works believe me
Best of luck
Gerry Bray Garden Collective