No, roaming in the United States is generally not free with EU, UK, or even most US mobile plans, and can incur significant charges.
For travelers from the EU or UK, "roam like at home" benefits apply only within the European Economic Area. When you travel to the United States, your existing plan will typically switch to international roaming rates, which are notoriously expensive for data, calls, and texts on major US networks like AT&T, T-Mobile, and Verizon. Even with a US-based plan, while you won't be "roaming" in the traditional sense, coverage can vary significantly by location, and some plans may have limitations or extra costs for extensive travel or specific services outside your primary coverage area.
To avoid bill shock, consider a local solution. An eSIM provides a convenient and cost-effective alternative, connecting you to strong local networks without the high roaming fees.