How the Washington and London treaties constrained cruisers differently

Did the Royal Navy have to destroy cruisers because of the Washington or London naval treaties?

No. Washington chiefly capped an individual cruiser at 10,000 tons, while the London treaties constrained overall numbers and helped drive the shift from County and Town classes toward smaller Crown Colony designs.

The Washington Naval Treaty did not impose a total cruiser count in the way the question assumes. Its decisive cruiser rule was the 10,000-ton ceiling for an individual ship. The London Naval Treaty then constrained the aggregate building program and curtailed further County-class construction. The second London agreement helped turn the Town-class trajectory toward the smaller Crown Colony class. Different treaty mechanisms affected quantity and design in different ways.