Whether or not the UK will leave the European Union remains to be seen, but it is a sufficiently serious prospect for it to be worth thinking about its implications for agricultural policy.
What one would probably have is a continuation of a version of the CAP at the national level. One of the constraints here is that the UK would still be a member of the World Trade Organisation and any agricultural subsidies it provided would have to be compatible with WTO rules. Indeed, it could be argued that recent changes to the CAP have been driven too much by the need to provide subsidies in a form that can demonstrate that they are compatible with the 'green box'/non-trade-distorting requirements of the WTO. Hence, the policy instruments may have been influenced too much by that requirement.
Within the discussion of the 'balance of competences' review of the CAP, one issue is how much 'renationalisation' there has been of the CAP. Certainly, there has been quite a considerable amount of recoupling which gives quite a lot of discretion to member states or their regional governments, but the basic principles of the CAP remain intact.
In any case, some would argue that the term 'renationalisation' is an inappropriate or old fashioned one. What has happened rather is the maintenance of a common policy design with national flexibility in policy implementation. Some argue that as the goals of the CAP have become more complicated, and in particular taken on a greater public goods/environmental emphasis, there has been a recasting of the form of the CAP (although it is possible to exaggerate the extent of this). What this requires is policy instruments that allow diversity of implementation in member states (but not to an extent that would satisfy Eurosceptics). It is, however, worth bearing in mind that a lot of policies affecting agriculture are nationally determined, particularly taxation and inheritance law and planning regulations.
It may be that the CAP can be characterised as a means of tackling the market failures associated with land management (but arguably a rather inefficient means of doing so). However, for some member states the occupation of land could be a key objective to prevent rural depopulation and secure the ecosystem benefits of farmed land.
One also comes up against the problem of a low level of competence in effective policy design and delivery. That is not a problem confined to the CAP, but is a general challenge for the EU and for member state governments, but it is particularly evident in relation to the CAP.