Re: Scrap it
There are typically a few arguments for subsidising farming:
1) A strategic decision to protect the food supply. The UK is already not self-sufficient in food production and decimating local food production would make the country even more dependent on imports. Food imports which may see a 20% import duty after Brexit if we screw up the negotiations.
2) These subsidies are often also used to steer behaviour. They can, for instance, force farmers to employ crop rotation techniques so the land isn't exhausted too quickly. Or they can pay for leaving certain plots of land uncultivated for conservation reasons. Through these mechanisms many countries have made farmers an integral part of environmental protection, flood prevention etc.
3) They can be a good money making scheme for people in the right places. Paul Dacre, the editor of the UK's biggest Neo-Nazi broadsheet, receives over €400.000 a year in EU subsidies for his estates.
In the current environment, arguments 1 and 3 will probably be enough to continue subsidising farming.