Odd, then, that the farmers who get paid by far the most in subsidies are the multimillionaire barley barons

Not really. the average farm size (94.7 ha) is nearly six times higher than the EU average (16.1 ha) But according to Saville's(2016)the average farm size(combinable crops) is just over 300 hectares.
30% of the direct payment allocation, paid per hectare, is linked to three environmentally-friendly farming practices: crop diversification, maintaining permanent grassland and dedicating 5 % of arable land to environmentally friendly measures (so-called 'ecological focus areas').
England has applied a basic payment at a flat rate according to three different types of land (defined as 'non-severely disadvantaged areas','lowlands & severely disadvantaged areas' and 'upland,other   moorland and moorland');
The more land you have the more dosh you get but arable farms, as explained. are larger and require greater capitilization to operate.
With sheep all you need is fencing (unless heft)and a dog or two.
A sheep costs nominally £100, a combine £125,000. There is also far more financial risk in arable farming.