Unless your polytunnel is really high a pinchbar (ours is about 6ft long) is not very useful - you are in danger of pushing it through the polythene above your head by accident... use a mattock or pick axe, just be careful when swinging.... we did that in ours. Then built raised beds, about 25 to 30cm high.
We found this year (10 years of use) though that the soil - despite regular dressings with manure - seems quite exhausted, as the beans/peas and beetroot all were terrible. Now planning on taking out a lot of soil, refilling with fresh topsoil, plus manure, seaweed and rock dust. One thing that probably contributed was that I left it going dry in winter usually.... not good, but as it's our hay storage unit as well it was difficult to keep wet.
I am quite sceptical wrt no-dig and heavy clay soil...