Royal Navy leverage during the American Civil War

Did Britain fear it could not fight the United States and Prussia together in the 1860s?

No; Prussia had little navy, and British sea power could have broken the Union blockade and supplied the Confederacy while ships such as HMS Warrior outmatched American monitors at sea.

The answer rejects the idea that Britain paid compensation because it feared a simultaneous naval war with Prussia and the United States. Prussia possessed little naval power, while the United States had just endured civil war and depended on its blockade of the Confederacy. A British intervention could have broken that blockade, supplied the South, and forced the Union to confront the world's largest navy. HMS Warrior and other British ironclads had a major open-ocean advantage over monitors, whose best chance required restricted waters that denied Warrior room to manoeuvre. Suspected Confederate ironclads building in Liverpool were bought into Royal Navy service once their destination became politically dangerous. A later question confirms that the United States had no convincing direct answer to Warrior during the war beyond experimenting with its own ocean-going ironclads. The combined discussion grounds the counterfactual in blockade logistics, sea-keeping, and the unequal global reach of the two fleets.