There are strict restrictions in place regarding travel to and from Wales during England's national lockdown between 5 November – 2 December. No person living outside Wales may enter or remain in Wales without a reasonable excuse. Whilst a person may have a 'reasonable excuse' to enter Wales for reasons such as work (which includes beating and picking up on shoots that may now take place in Wales), you may not enter Wales in order to participate in a shoot.
The Health Protection (Coronavirus, Restrictions) (England) (No. 4) Regulations 2020, which brought in the current lockdown in England makes it clear that: 'No person may leave or be outside of the place where they are living without reasonable excuse'. This enables them to visit a public outdoor space for the purposes of open air recreation either:
None of these exemptions have any relevance to driven / organised game shooting. Game shooting is clearly not 'work', nor is it 'education, and no court would think otherwise.
During this second lockdown in England, leaving one's home for the purpose of recreation outdoors with a larger group of people from different households is against English law. It does not matter where the recreation is intended to occur, nor what the law says in Wales. The moment you leave your home in England without reasonable excuse, as defined in the regulations, you commit an offence.