The main US tax issue is whether or not your UK business has a "permanent establishment" in the US - which is defined by the tax treaty between the US and the UK. If you have any kind of physical presence in the US - an employee, an office or even someone working on your behalf - then you probably have a permanent establishment, which means you have to pay US tax on profits attributable to that permanent establishment, and that tax is credited against the UK tax on those profits. If you don't have anybody or any physical presence in the US, then you probably don't have a permanent establishment. But you may still have to file a US tax return reporting nil taxable profits and claiming the protection of the treaty.

Even if you do not have a federal tax liability, it is possible that you would have a Florida state tax liability, depending on the precise facts.

If your UK business is a company, you would need a US EIN (employer Identifcation Number) for the company to file its US tax return. If you do business as a sole trader, you use your ITIN (or SSN if you have one).

Needless to say, this can be a tricky area, so you need to get good tax advice in both the UK and the US.