Contact cajon makers directly to find cajons made made in the UK. Unfortunately most big online stores and many music stores only carry imported brands. Buying a locally made cajon cyles your income back through your local economy. Below are links the cajon makers in the UK:

You may be able to minimize the carbon footprint of your cajon purchase by buying a locally produced cajon. Check out this link to learn more: Mitigate Climate Change. Most imported cajons are shipped around the planet in big cargo ships. A locally made cajon helps your local economy and demonstrates that you are thinking about and helping local craftsmen.

YouTube playlist of cajons made in the UK:
Note that not all manufacturers have current YouTube videos. The list on this page includes websites and Facebook pages which may contain videos not on YouTube. The list on this page is current and actively maintained, the YouTube playlist is less frequently updated.

One photo per United Kingdom cajon manufacturer in Pinterest:

Listed above are links to the cajon drum builders in the United Kingdom as retrieved by Internet searches from March to April 2020. I am sure there are many others not listed. Please send me updates and correction if you have additional information. Thanks.