Tribal-class destroyer Atlantic range

Did Tribal-class destroyers have trouble crossing the Atlantic without refueling?

No; their nominal range covered the crossing comfortably, while operational maneuvering was the larger fuel burden.

A Tribal's stated 5,700-nautical-mile range left a large theoretical margin over the roughly 2,600-nautical-mile crossing from Rosyth to Halifax. The operational fuel problem came from maneuvering and sustained activity after arrival, not simply traversing the ocean. Published range should not be confused with endurance under high-speed wartime operations. The nominal figure was sufficient for the crossing itself.