UK tax on US shares

Dividends are taxed differently to normal income. However, if your total income from salary and dividends is less than your personal allowance then you won’t pay tax on it. Also, the first Β£2000 of dividends is also tax-free.

But if you are self-employed, you might well need to do a self-assessment anyway. Self Assessment tax returns: Who must send a tax return - GOV.UK