Yes, a UK citizen can move to the USA permanently.
It starts with a green card. A green card will grant give you permanent lawful residence, but it will not allow you stay in the United States indefinitely. You will need to renew your green card every ten years. However, you can apply for US citizenship after a set number of years as a lawful permanent resident.
Retiring to the US from the UK there are limited options. One of the following;
1. Family member sponoring them (who is a US citizen)
2. Green Card Lottery – very low chance of success
3. EB-5 investor program requiring an investment of at least 500,000 USD. It’s not actually a retirement related visa, as it is open to anyone willing to make the investment. But it is essentially the only option for most retirees who do not qualify for any other way of getting a green card.
Make sure you get the right expert help, as incorrect applications can spell disaster.