From bfi.org.uk:
“Productions
Is production allowed to take place at the moment?
As of January 5 2021, production is able to continue under lockdown restrictions currently in place in all four nations of the UK, so long as productions follow proper guidelines that allow them to do so safely. These were developed by the British Film Commission in consultation with industry as part of the Screen Sector Taskforce’s work. Find out more.
The British Film Commission will be updating their guidance in due course in response to the current situation, so please check regularly for updates.
The guidelines complement production guidance by ITV, BBC, Sky, Channel 4, Channel 5, STV, ITN, the Commercial Broadcasters Association (COBA) and Pact concerning wider TV programme making in every genre. Find out more.
The UK Screen Alliance has also consulted with industry to develop guidelines for VFX and post-production. Find out more.”