Yes, agricultural land is classified in England and Wales too, and the classification will give you a good indication of its likely productivity for crops other than grass.
If it's just a veg plot for the house you want, you'll probably be fine almost anywhere (although some types of ground are better for some crops than other, of course), maybe with windbreaks, soil improvements, poly tunnel, etc. But if your plan is to grow things to sell, then you probably do want to get the classifications and do a proper assessment. For instance, our clay ground here in North Cornwall grows quite a bit of veg for the community (there are 30 of us here on 32 acres), but we've been advised that field crops, even for a bit of winter feed for the livestock, doesn't make much sense here. The land grows good grass which grows good livestock, so we grow our own meat and milk, and crop our own hay for them for winter.