Do I have to use the double taxation treaty on a very small UK income?

I'm a UK citizen currently resident in the United States. I have a small amount of bank interest from the UK (less than £4,000). I have declared this on my US tax return as part of my worldwide earnings and will be taxed on it in the US. As it's well below the single person allowance in the UK, is there any point in me going through the double taxation treaty process? Or just submit a standard Self Assessment with this income (obviously using third-party software as non-UK residents cannot file on the HMRC website). Thanks for any help that anyone can give me.

Hi,

The threshold for declaring the interest in a tax return is £10000. As you are below this threshold and you do not meet any other criteria for completing a tax return, a letter confirming the interest and the accounts it came from is sufficient. If you do meet the criteria for completing a tax return, then this interest must also be included.

Thank you.