What's the point of the subsidy? Why not pay the actual price at point of purchase.
Is it simply a case of remaining competitive with cheaper imports as it appears to be?
Yes its about staying competitive but other consequences too. Food prices wouldn't go up it would just get imported and uk farmers would go out of business. There's a massive secondary agri industry, rural jobs are the most difficult to replace, land would go to rack and ruin, imported food of questionable quality and husbandry, money spent on food (think how much) going straight out the country. Also politically not being able to feed ourselves (or regulate) was/is considered a scary prospect.
Subsidies started as buying produce(remember butter mountains and wine lakes) and paying per head maintained to artificially raise prices. Result not surprisingly was increased production and vicious circle. Now they just finished the transition to area based under the provision you farm sustainably (if you want to) but always maintain land in good condition. A large proportion is also given in grants for diversifying or organic and the like.
Re dairy, don't know much about that but I always thought a quota was a limiter. You don't get subsidy for it, rather you get a levy unless you have a quota. Would guess dairy farmers make cash & subsidy from selling the calves that keep the mothers milking. The horror of it all.