this may be wrong but this is how i see it working. someone more knowledgeable may dispute this.
Usually income is sourced where it is earned. primary taxing rights fall to the country of residence under the US/UK treaty so (presumably) the UK. If you are working for a US company, being paid locally, you should be able to qualify for the foreign earned income exclusion or foreign tax credit. so you could be paid as freelance by the US company, and the self employment tax, the "totalisation agreement" with the US/UK, you can get out of US self-employment tax.. you file in the UK, but pay tax to the UK.