What country in history adopted the most purely laissez faire-type economic policy?

A good case could be made for Victorian England. The repeal of the Corn Laws, the reduction in other tariffs (leading to complete free trade), the eradication of most indirect taxes and a minimal income tax all led to a tiny role for government. As Matthew Arnold wrote in Culture and Anarchy (1869):

...we are left with nothing but our system of checks, and our notion of its being the great right and happiness of an Englishman to do as far as possible what he likes, we are in danger of drifting towards anarchy. We have not the notion, so familiar on the Continent and to antiquity, of the State--the nation in its collective and corporate character, entrusted with stringent powers for the general advantage, and controlling individual wills in the name of an interest wider than that of individuals.

Despite some social reforms during the Edwardian period, the Victorian structure remained in essentials up until the First World War. A. J. P. Taylor famously wrote in his English History:

Until August 1914 a sensible, law-abiding Englishman could pass through life and hardly notice the existence of the state, beyond the post office and the policeman. He could live where he liked and as he liked. He had no official number or identity card. He could travel abroad or leave his country for ever without a passport or any sort of official permission. He could exchange his money for any other currency without restriction or limit. He could buy goods from any country in the world on the same terms as he bought goods at home. For that matter, a foreigner could spend his life in this country without permit and without informing the police. Unlike the countries of the European continent, the state did not require its citizens to perform military service. An Englishman could enlist, if he chose, in the regular army, the navy, or the territorials. He could also ignore, if he chose, the demands of national defence. Substantial householders were occasionally called on for jury service. Otherwise, only those helped the state who wished to do so. The Englishman paid taxes on a modest scale: nearly £200 million in 1913-14, or rather less than 8 per cent of the national income. The state intervened to prevent the citizen from eating adulterated food or contracting certain infectious diseases. It imposed safety rules in factories, and prevented women, and adult males in some industries, from working excessive hours. The state saw to it that children received education up to the age of 13. Since 1 January 1909, it provided a meagre pension for the needy over the age of 70. Since 1911, it helped to insure certain classes of workers against sickness and unemployment...Still, broadly speaking, the state acted only to help those who could not help themselves. It left the adult citizen alone.