When Allied warships replenished one another at sea

Was it common for U.S. and Royal Navy supply ships to replenish each other's warships?

Yes, especially during long operations in the Indian Ocean and Far East; shorter Mediterranean sorties often returned to port before food and fuel became the limiting factor.

Cross-support and at-sea replenishment were normal where fleets operated far from bases for extended periods. Mediterranean forces could often return to port after a short sortie, although they might run dangerously low on ammunition, while Indian Ocean and Far Eastern operations made fuel, food, and stores transfer routine. The comparison highlights operational geography as the driver of fleet-train demand. Allied practice followed distance and endurance rather than a rigid rule about whose supply ship served which navy.