Paying USA Freelance Taxes in US or UK?

I wonder if anyone has freelance income from the US that they pay tax on to the IRS rather than recording it on HMRC Self-Assessment to avoid double taxation and to pay MUCH LESS tax on that income. In my case, it is only $5000 for the year, as the rest of my income is from Social Security which I do pay UK tax on. Many thanks for any advice.

You should find a tax forum to ask these questions as they are not immigration related, which is for immigration related questions only.