I don't think the problem with ohc cars was poor reliability so much as expensive maintenance bills.
In 1931 there were only four family cars (British or Continental) on the British market under 12hp (RAC rating) that were not side-valve: the long-wheelbase Morris Minor(which retained the ohc engine after the side-valve engine was adopted for the more popular models), the Riley Nine, the Rover 10/25, and the Singer Junior. Even by the outbreak of war, the majority of small family cars were still side-valve (Ford, Morris, Standard, as well as Austin) - they were just so much cheaper to manufacture (and maintain)!