Not necessarily; we could very well keep our high standards which would be fine for exporting to places with less stringent standards, whilst increasing the standards of imported meats if we were importing more from the EU again, as opposed to importing from Asia for meats used in ready meals, takeaways, etc.
I work for a food manufacturer which used to sell 40% of made good to the EU. I say used to. The added costs has meant we have to increase sale prices which when selling to companies like Carrefour means they just refuse when they can source the same product on the EU for less.
The type of food we make (non animal except for honey and milk) aren't really imported into the UK. The sales to UK haven't really been affected. The business is struggling to break even.
I think the company will survive but it means making big changes in ways not done before to increase sales to the UK market. Interesting times...