If you're a UK-based sole trader invoicing a U.S. company for services performed outside the U.S., you generally don’t need an ITIN and have no U.S. tax filing requirement. The U.S.–UK tax treaty usually exempts this kind of income from U.S. withholding tax.

To make that clear to the U.S. company, you can complete a W-8BEN form (not W-7), which certifies you're a non-U.S. person and claim treaty benefits. The W-7 is only for applying for an ITIN, which you shouldn't need unless you're earning U.S.-sourced income inside the U.S.

So, unless you're physically working in the U.S. or receiving U.S.-sourced passive income, you don’t need an ITIN, just submit the W-8BEN to them.