I'm sure you're aware of the Prime Minister's announcement about the latest national lockdown in England, as well as First Minister Nicola Sturgeon's announcement regarding Scotland in the last 24hrs or so.

I wanted to make sure you’re aware that home-moving can continue, whether you're in England, Wales or Scotland.

England
The government has today issued updated guidance around the restrictions in England coming into effect (Tuesday 5th January 2021). Here’s the key information that will affect you:
Moving home
You can still move home. People outside your household or support bubble should not help with moving house unless absolutely necessary. Estate and letting agents and removals firms can continue to work. If you are looking to move, you can go to property viewings. Follow the national guidance on moving home safely, which includes advice on social distancing, letting fresh air in, and wearing a face covering.

Here's a full summary of the latest guidance direct from the government which covers other industries as well;

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/949536/NationalLockdownGuidance.pdf