Question: During what war were the Russia-United Kingdom relations in a state of rivalry after the abdication of Emperor Nicholas II? 

Context:
Grand Duke Vladimir Alexandrovich of Russia
Grand Duke Vladimir Alexandrovich of Russia ("Влади́мир Александрович") ) (22 April 1847 – 17 February 1909) was a son of Emperor Alexander II of Russia, a brother of Emperor Alexander III of Russia and the senior Grand Duke of the House of Romanov during the reign of his nephew, Emperor Nicholas II.
Grand Duke Sergei Alexandrovich of Russia
Grand Duke Sergei Alexandrovich of Russia ("Сергей Александрович"; May 11, 1857 – February 17, 1905) was the fifth son and seventh child of Emperor Alexander II of Russia.
 He was an influential figure during the reigns of his brother Emperor Alexander III of Russia and his nephew Emperor Nicholas II, who was also his brother in law through Sergei's marriage to Elizabeth the sister of Tsarina Alexandra.
Charles Sydney Gibbes
Charles Sydney Gibbes (19 January 1876 – 24 March 1963) was a British academic who from 1908 to 1917 served as the English tutor to the children of Emperor Nicholas II of Russia.
 When Nicholas abdicated the throne in March 1917 Gibbes voluntarily accompanied the Imperial family into exile to the Siberian village of Tobolsk.
 After the family was murdered in 1918 Gibbes returned to the United Kingdom and eventually became an Orthodox monk, adopting the name of "Nicholas" in commemoration of Nicholas II.
 He died in 1963, and is buried at Headington cemetery, Oxford, Oxfordshire, England.
October Manifesto
The October Manifesto (Russian: Октябрьский манифест, Манифест 17 октября ), officially The Manifesto on the Improvement of the State Order (Манифест об усовершенствовании государственного порядка), is a document that served as a precursor to the Russian Empire's first constitution, which would be adopted the next year.
 The Manifesto was issued by Emperor Nicholas II, under the influence of Sergei Witte, on 30 October [O.S. 17 October] 1905 as a response to the Russian Revolution of 1905.
 Nicholas strenuously resisted these ideas, but gave in after his first choice to head a military dictatorship, Grand Duke Nicholas, threatened to shoot himself in the head if the Tsar did not accept Witte's suggestion.
 Nicholas reluctantly agreed, and issued what became known as the October Manifesto, promising basic civil rights and an elected parliament called the Duma, without whose approval no laws were to be enacted in Russia in the future.
 According to his memoirs Witte did not force the Tsar to sign the October Manifesto, which was proclaimed in all the churches.
Russia–United Kingdom relations
The Russia–United Kingdom relations (Russian: Российско-британские отношения ) is the relationship between the Russian Federation and the United Kingdom of Great Britain and Northern Ireland and it's overseas territories.
 Spanning nearly five centuries, it has often switched from a state of alliance to rivalry or even war.
 The Russians and British were allies against Napoleon, and enemies in the Crimean War of the 1850s, and rivals in the Great Game for control of central Asia in the late 19th century.
 They were allies again in World Wars I and II, although relations were strained by the Russian Revolution of 1917.
 They were at sword's point during the Cold War (1947–91).
 Russian big businesses had strong connections with the City of London and British corporations during the late 1990s and 2000s.
Ural State Mining University
Ural State Mining University (Russian: Уральский государственный горный университет ) is situated in Yekaterinburg, Russian Federation.
 It was founded in 1914.
 In 1917 Nicholas II signed an order titled "On keeping of the Yekaterinburg Institute of Mines under the patronage of His Majesty the Emperor and on giving to this educational establishment the title of "The Emperor Nicholas II Ural Institute of Mines"".
Nicholas II of Russia
Nicholas II or Nikolai II (Russian: Николай II Алекса́ндрович , "Nikolay II Aleksandrovich" ; 18 May [O.S. 6 May] 1868 – 17 July 1918) was the last Emperor of Russia, ruling from 1 November 1894 until his forced abdication on 15 March 1917.
 His reign saw the fall of the Russian Empire from being one of the foremost great powers of the world to economic and military collapse.
 Due to the Khodynka Tragedy, anti-Semitic pogroms, Bloody Sunday, the violent suppression of the 1905 Revolution, the execution of political opponents and his perceived responsibility for the Russo-Japanese War, he was given the nickname Nicholas the Bloody by his political adversaries.
 Soviet historiography portrayed Nicholas as a weak and incompetent leader, whose decisions led to military defeats and the deaths of millions of his subjects.
Prince Andrew Romanov
Prince Andrew Andreyevich Romanov (born 21 January 1923) is a Russian American artist and author.
 He is a grand-nephew of Russia's last Emperor, Nicholas II.
 Since December 31, 2016 he is a claimant to the headship of the Imperial House of Russia and President of the Romanov Family Association.
 He is a great-great-grandson in the male-line of Emperor Nicholas I of Russia.
Russian Revolution
The Russian Revolution was a pair of revolutions in Russia in 1917 which dismantled the Tsarist autocracy and led to the rise of the Soviet Union.
 The Russian Empire collapsed with the abdication of Emperor Nicholas II and the old regime was replaced by a provisional government during the first revolution of February 1917 (March in the Gregorian calendar; the older Julian calendar was in use in Russia at the time).
 Alongside it arose grassroots community assemblies (called 'soviets') which contended for authority.
 In the second revolution that October, the Provisional Government was toppled and all power was given to the soviets.
Grand Duke Alexander Alexandrovich of Russia
Grand Duke Alexander Alexandrovich of Russia (Russian: Великий Князь Александр Александрович Романов; 7 June 1869 – 2 May 1870) was the infant son of Emperor Alexander III–the heir apparent, styled "Tsesarevich", to the Russian throne as the eldest living son of Emperor Alexander II–and his consort, Marie Fyodorovna of Russia.
 He was Alexander and Marie's second child, second son, and the younger brother of the future Emperor Nicholas II.
 He died of meningitis in 1870, one month before his first birthday.
 "The doctors maintain he did not suffer, but we suffered terribly to see and hear him," his mother wrote to her own mother, Queen Louise of Denmark.

Answer: the Cold War (1947–91)