There is very little point is discussing food prices in or out of the UK without having some knowledge of the CAP and how much it contributes to farmers incomes (   
farmers welfare! )   
Direct payments benefit nearly 7 million farms throughout the. European Union and often represent an important share of their agricultural income (on average, nearly half of farmers' income in the last ten years came from this ..
The lion's share (72%) of the current EU farm budget is dedicated to direct payments for European farmers. ... On average direct payments amount to ?267 per eligible hectare.

The CAP benefits large landowners just for owning more land. EU protectionism on agriculture has been criticised for the costs it imposes on consumers through higher food prices and the costs it imposes on developing countries by making it difficult for them to compete with EU farmers.

The current Government says it will continue to make payments to UK farmers on the same basis as now until 2020. Negotiations are already underway within the EU on how to reform the next round of CAP, so the CAP will change in any case (and may need substantial reform given the budget shortfall post-Brexit). 14.1% less rebate. Should subsidies shrink post 2020 prices will inevitably rise to accommodate at least a component of the resulting shortfall in income.
Happy Days ahead!

Essentially very few farms in the EU are viable without CAP support.
This has to reform for 2020 to implement the next round.
Until this next round is thrashed out the outcome and it's impact on food prices in or out of the EU is totally unknown territory.