@Mike-And-Jane0 Here in the US there is the ability to report foreign taxes paid on one's tax return in order to have that credited against one's total tax liability.
I'd be surprised if the same scenario isn't present on UK tax forms (or any other country's tax forms). I'm not suggesting someone enter the US tax system and file a US tax return. I'm suggesting people file a tax return as they normally would, in their home country, and request a credit for foreign taxes paid on the income they were going to report on their local tax return anyway, so they don't get taxed twice.
https://www.gov.uk/tax-foreign-income/paying-tax
The tax treaties between countries generally include language that prevents double taxation on income.
Once withholdings are deducted, they are, essentially, money owed to the IRS, which a company is liable to pay over, irrespective of whether it was a calculation error, incorrect deduction or any other scenario. They don't get refunded directly.
This can, of course, be confirmed by contacting a local tax professional. Perhaps someone should reach out to their friendly local accountant, ask the question, and post the response.