Re: "what happens..native UK farming industry if..reduce import tariffs to 0?" " ...
But the UK had to "industrialize" it's farming during WWII.
As a result it's got a relatively small number of very large (by European standards) farm holdings in a small number of hands.
It's not that simple.
It's been a tradition in England for centuries that the eldest son inherited the farm, and other children had to do something else (hence the stereotype that the 2nd son went into the army, and the third entered the church). That model ensured that farms remained intact, and large, and over time, as people bought neighbouring farms, the overall size increased.
In other countries, France as an obvious example, that practice is illegal. The law requires that all children inherit equally, so when a farmer with 4 children dies the farm is necessarily cut into 4 pieces and shared out. Even if one child can raise the money to buy out a sibling this still tends to keep farms small, fragmented, and uneconomic. It's almost impossible to create a large farm in such countries, hence the huge tax subsidies handed out to keep such small farms going. This imbalance in the CAP is one of the reasons that the UK rebate was negotiated, because UK farmers received far less in subsidy than their continental equivalents. If left to operate solely on their own merits the UK farming sector would be in far better economic health than those in most of the EU.
Standardizing inheritance rules across the EU would of course be a way to "solve" this, but would clearly be politically impossible. Like so many things (taxes, pensions, etc.) it shows why the "union" is just a pipe dream, and why all those tax-funded eurocrats can only nibble at the edges of a true common Europe by tweaking the trivial stuff, like mobile phone roaming charges.